{"text_format":"3","workbook":"xlsx","n_sheets":7,"sheets":["Porous Absorber","Perforated Panel","Slotted Panel","Microperforated Panel","Flow Resistivity","Configuration","Acknowledgements"],"not_rendered":{"charts":4,"images":33,"macros":1,"defined_names":95},"read":"whole","date_system":"1900"}

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[" "]
[null,"Rigid Backed Porous Absorber",{"$nulls":4},"© Chris Whealy 2020","V1.60"]
[null,"Properties of absorber",{"$nulls":4},"Display options",{"$nulls":8},"Rigid Backed Porous Absorber"]
[null,"Absorber thickness (ta)",{"v":30,"d":"30.0"},"mm",{"$f":"porous_abs_thickness_mm/25.4","v":{"v":1.1811023622047245,"d":"1.181"}},"in","Start graph at",62.5,"Hz",{"$nulls":6},"Absorber thickness (ta)",{"$f":"porous_abs_thickness_mm/1000","v":0.03},"m","cos(y)",{"$f":"COS(porousAbsAngle*PI()/180)","v":{"v":1,"d":"1.0000"}}]
[null,"Absorber flow resisitivity",{"v":16500,"d":"16,500"},"rayls/m",{"$nulls":6},"To see the graph in the standard",{"$nulls":4},"Air gap (l)",{"$f":"porous_airGap_mm/1000","v":0.1},"m"]
[null,"Properties of cavity",{"$nulls":8},"analysis frequencies, select",{"$nulls":4},"Octave subdivisions",6]
[null,"Air gap (d)",{"v":100,"d":"100.0"},"mm",{"$f":"porous_airGap_mm/25.4","v":{"v":3.937007874015748,"d":"3.937"}},"in","Show subdivisions of",{"$nulls":3},"\"Whole Octaves\" and set the"]
[null,"Properties of incident sound",{"$nulls":8},"starting frequency to 62.5Hz",{"$nulls":4},"Interval number",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]
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[{"$nulls":14},"2pf","Angular frequency (w)",{"$f":"2*PI()*Q9","v":{"v":392.6990816987241,"d":"392.7"}},{"$f":"2*PI()*R9","v":{"v":440.7898156127599,"d":"440.8"}},{"v":494.76983930660913,"d":"494.8"},{"v":555.3603672697959,"d":"555.4"},{"v":623.3709353955011,"d":"623.4"},{"v":699.7102170005635,"d":"699.7"},{"v":785.3981633974486,"d":"785.4"},{"v":881.5796312255201,"d":"881.6"},{"v":989.5396786132183,"d":"989.5"},{"v":1110.7207345395918,"d":"1110.7"},{"v":1246.7418707910022,"d":"1246.7"},{"v":1399.4204340011272,"d":"1399.4"},{"v":1570.7963267948974,"d":"1570.8"},{"v":1763.1592624510401,"d":"1763.2"},{"v":1979.0793572264367,"d":"1979.1"},{"v":2221.4414690791864,"d":"2221.4"},{"v":2493.4837415820048,"d":"2493.5"},{"v":2798.8408680022544,"d":"2798.8"},{"v":3141.5926535897947,"d":"3141.6"},{"v":3526.3185249020808,"d":"3526.3"},{"v":3958.1587144528735,"d":"3958.2"},{"v":4442.882938158369,"d":"4442.9"},{"v":4986.9674831640095,"d":"4987.0"},{"v":5597.68173600451,"d":"5597.7"},{"v":6283.18530717959,"d":"6283.2"},{"v":7052.6370498041615,"d":"7052.6"},{"v":7916.317428905749,"d":"7916.3"},{"v":8885.765876316738,"d":"8885.8"},{"v":9973.934966328012,"d":"9973.9"},{"v":11195.36347200902,"d":"11195.4"},{"v":12566.370614359183,"d":"12566.4"},{"v":14105.274099608312,"d":"14105.3"},{"$f":"2*PI()*AW9","v":{"v":15832.634857811498,"d":"15832.6"}},{"v":17771.53175263348,"d":"17771.5"},{"v":19947.86993265604,"d":"19947.9"},{"v":22390.72694401802,"d":"22390.7"},{"v":25132.741228718387,"d":"25132.7"},{"v":28210.54819921663,"d":"28210.5"},{"v":31665.269715623002,"d":"31665.3"},{"v":35543.06350526696,"d":"35543.1"},{"v":39895.73986531208,"d":"39895.7"},{"v":44781.45388803605,"d":"44781.5"},{"v":50265.48245743669,"d":"50265.5"},{"v":56421.09639843326,"d":"56421.1"},{"v":63330.539431246005,"d":"63330.5"},{"v":71086.12701053394,"d":"71086.1"},{"v":79791.47973062418,"d":"79791.5"},{"v":89562.9077760721,"d":"89562.9"},{"v":100530.96491487339,"d":"100531.0"}]
[null,"This plot is a simplification of reality because it is only calculated for sound incident at exactly the specified angle.",{"$nulls":12},"2p/l","Wave number (kair)",{"$f":"TwoPiByC*Q9","v":{"v":1.1436219656127162,"d":"1.1436"}},{"v":1.2836722540132413,"d":"1.2837"},{"v":1.4408733875976119,"d":"1.4409"},{"v":1.617325693997281,"d":"1.6173"},{"v":1.815386711267567,"d":"1.8154"},{"v":2.037702686403008,"d":"2.0377"},{"v":2.287243931225433,"d":"2.2872"},{"v":2.5673445080264834,"d":"2.5673"},{"v":2.8817467751952237,"d":"2.8817"},{"v":3.234651387994562,"d":"3.2347"},{"v":3.630773422535134,"d":"3.6308"},{"v":4.075405372806017,"d":"4.0754"},{"v":4.574487862450867,"d":"4.5745"},{"v":5.134689016052967,"d":"5.1347"},{"v":5.763493550390449,"d":"5.7635"},{"v":6.4693027759891315,"d":"6.4693"},{"v":7.261546845070269,"d":"7.2615"},{"v":8.150810745612034,"d":"8.1508"},{"v":9.148975724901735,"d":"9.1490"},{"v":10.269378032105935,"d":"10.2694"},{"v":11.526987100780898,"d":"11.5270"},{"v":12.938605551978252,"d":"12.9386"},{"v":14.52309369014054,"d":"14.5231"},{"v":16.30162149122407,"d":"16.3016"},{"v":18.29795144980347,"d":"18.2980"},{"v":20.53875606421187,"d":"20.5388"},{"v":23.0539742015618,"d":"23.0540"},{"v":25.877211103956505,"d":"25.8772"},{"v":29.046187380281054,"d":"29.0462"},{"v":32.603242982448144,"d":"32.6032"},{"v":36.59590289960695,"d":"36.5959"},{"v":41.077512128423706,"d":"41.0775"},{"$f":"TwoPiByC*AW9","v":{"v":46.1079484031236,"d":"46.1079"}},{"v":51.75442220791302,"d":"51.7544"},{"v":58.092374760562166,"d":"58.0924"},{"v":65.20648596489623,"d":"65.2065"},{"v":73.19180579921395,"d":"73.1918"},{"v":82.15502425684743,"d":"82.1550"},{"v":92.21589680624722,"d":"92.2159"},{"v":103.50884441582603,"d":"103.5088"},{"v":116.18474952112433,"d":"116.1847"},{"v":130.41297192979246,"d":"130.4130"},{"v":146.38361159842768,"d":"146.3836"},{"v":164.31004851369485,"d":"164.3100"},{"v":184.43179361249443,"d":"184.4318"},{"v":207.01768883165212,"d":"207.0177"},{"v":232.3694990422487,"d":"232.3695"},{"v":260.825943859585,"d":"260.8259"},{"v":292.76722319685535,"d":"292.7672"}]
[{"$nulls":15},"Properties of porous absorber"]
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[{"$nulls":15},"Impedence values"]
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[{"$nulls":15},"Reflection/Absorption (No air gap)"]
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[{"$nulls":15},"Impedence values"]
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[{"$nulls":15},"Ratio of wavenumbers (kair:kair x)",{"$f":"IMDIV(Q11,Q31)","v":"0.999999999999997"},{"$f":"IMDIV(R11,R31)","v":"1"},"1","1","0.999999999999998","0.999999999999999","1","1","1","1","0.999999999999998","0.999999999999999","0.999999999999999","0.999999999999999","1","1","1","1","1","1","1","1","1","0.999999999999998","0.999999999999998","0.999999999999999","1","1","1","1","1","1","1","1","0.999999999999999","1","0.999999999999999","1","1","1","1","1","0.999999999999998","0.999999999999999","1","1","0.999999999999999","1","1"]
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[{"$nulls":14},"Eq 1.28","At top of porous absorber (za + air)",{"$f":"IMDIV(IMSUM(IMPRODUCT(Q35,Q34),IMPRODUCT(Q14,Q14)),IMSUM(Q34,Q35))","v":"426.179599203616-2690.20185520718j"},"422.831230242817-2383.55480175778j","419.105442218686-2110.08980385473j","415.15870688058-1866.04232422363j","411.131449031844-1648.05739936008j","407.151518415032-1453.14295178252j","403.337662379051-1278.62799477057j","399.80314177466-1122.12510775771j","396.659675493666-981.496598280441j","394.021967110494-854.823786425303j","392.013175562454-740.378845301881j","390.771867396118-636.598598237491j","390.461278484839-542.059597037298j","391.282206251961-455.453664463635j","393.491717599146-375.562843840305j","397.431428303116-301.232306326162j","403.572086649789-231.339147439899j","412.58711818732-164.754087116401j","425.480262761037-100.291957434487j","443.820498134521-36.6464997330683j","470.205692215294+27.6893201386473j","509.258364417547+94.4783485715801j","569.99630565052+165.522730515678j","672.205082730924+240.718966159413j","865.480168054931+304.508341039144j","1268.53269014864+219.554413127541j","1490.25106285076-675.80493624601j","477.884928080102-841.482408590109j","247.626923776496-378.882620866078j","301.086464203435-108.579221740634j","450.137816819834+43.4874696151163j","691.657961873077+25.7672702179738j",{"$f":"IMDIV(IMSUM(IMPRODUCT(AW35,AW34),IMPRODUCT(AW14,AW14)),IMSUM(AW34,AW35))","v":"727.566865862318-315.897920643178j"},"359.39792224829-327.662744545319j","298.551133669263-32.224586551915j","612.357032958594+37.6817916223431j","457.946202647364-238.937642045449j","335.939171829191-17.5287579654926j","643.790610898013-78.9374433166363j","360.333531770401-64.6311155257107j","606.748503512693-58.9184465101612j","387.536197370957-2.62155773675925j","429.372058073786-152.207882420422j","523.446055825231-67.5841504727531j","487.243580726995+23.7377908030267j","455.329316092084+24.6649178207911j","472.570449053915+5.19943351381336j","481.326624260008-50.6529382834762j","405.77606849844-57.5274460410629j"]
[{"$nulls":15},"Real part of impedance (With air gap)",{"$f":"IMREAL(Q36)","v":{"v":426.179599203616,"d":"426.18"}},{"v":422.831230242817,"d":"422.83"},{"v":419.105442218686,"d":"419.11"},{"v":415.15870688058,"d":"415.16"},{"v":411.131449031844,"d":"411.13"},{"v":407.151518415032,"d":"407.15"},{"v":403.337662379051,"d":"403.34"},{"v":399.80314177466,"d":"399.80"},{"v":396.659675493666,"d":"396.66"},{"v":394.021967110494,"d":"394.02"},{"v":392.013175562454,"d":"392.01"},{"v":390.771867396118,"d":"390.77"},{"v":390.461278484839,"d":"390.46"},{"v":391.282206251961,"d":"391.28"},{"v":393.491717599146,"d":"393.49"},{"v":397.431428303116,"d":"397.43"},{"v":403.572086649789,"d":"403.57"},{"v":412.58711818732,"d":"412.59"},{"v":425.480262761037,"d":"425.48"},{"v":443.820498134521,"d":"443.82"},{"v":470.205692215294,"d":"470.21"},{"v":509.258364417547,"d":"509.26"},{"v":569.99630565052,"d":"570.00"},{"v":672.205082730924,"d":"672.21"},{"v":865.480168054931,"d":"865.48"},{"v":1268.53269014864,"d":"1268.53"},{"v":1490.25106285076,"d":"1490.25"},{"v":477.884928080102,"d":"477.88"},{"v":247.626923776496,"d":"247.63"},{"v":301.086464203435,"d":"301.09"},{"v":450.137816819834,"d":"450.14"},{"v":691.657961873077,"d":"691.66"},{"$f":"IMREAL(AW36)","v":{"v":727.566865862318,"d":"727.57"}},{"v":359.39792224829,"d":"359.40"},{"v":298.551133669263,"d":"298.55"},{"v":612.357032958594,"d":"612.36"},{"v":457.946202647364,"d":"457.95"},{"v":335.939171829191,"d":"335.94"},{"v":643.790610898013,"d":"643.79"},{"v":360.333531770401,"d":"360.33"},{"v":606.748503512693,"d":"606.75"},{"v":387.536197370957,"d":"387.54"},{"v":429.372058073786,"d":"429.37"},{"v":523.446055825231,"d":"523.45"},{"v":487.243580726995,"d":"487.24"},{"v":455.329316092084,"d":"455.33"},{"v":472.570449053915,"d":"472.57"},{"v":481.326624260008,"d":"481.33"},{"v":405.77606849844,"d":"405.78"}]
[{"$nulls":15},"Imaginary part of impedence (With air gap)",{"$f":"IMAGINARY(Q36)","v":{"v":-2690.20185520718,"d":"-2690.20"}},{"v":-2383.55480175778,"d":"-2383.55"},{"v":-2110.08980385473,"d":"-2110.09"},{"v":-1866.04232422363,"d":"-1866.04"},{"v":-1648.05739936008,"d":"-1648.06"},{"v":-1453.14295178252,"d":"-1453.14"},{"v":-1278.62799477057,"d":"-1278.63"},{"v":-1122.12510775771,"d":"-1122.13"},{"v":-981.496598280441,"d":"-981.50"},{"v":-854.823786425303,"d":"-854.82"},{"v":-740.378845301881,"d":"-740.38"},{"v":-636.598598237491,"d":"-636.60"},{"v":-542.059597037298,"d":"-542.06"},{"v":-455.453664463635,"d":"-455.45"},{"v":-375.562843840305,"d":"-375.56"},{"v":-301.232306326162,"d":"-301.23"},{"v":-231.339147439899,"d":"-231.34"},{"v":-164.754087116401,"d":"-164.75"},{"v":-100.291957434487,"d":"-100.29"},{"v":-36.6464997330683,"d":"-36.65"},{"v":27.6893201386473,"d":"27.69"},{"v":94.4783485715801,"d":"94.48"},{"v":165.522730515678,"d":"165.52"},{"v":240.718966159413,"d":"240.72"},{"v":304.508341039144,"d":"304.51"},{"v":219.554413127541,"d":"219.55"},{"v":-675.80493624601,"d":"-675.80"},{"v":-841.482408590109,"d":"-841.48"},{"v":-378.882620866078,"d":"-378.88"},{"v":-108.579221740634,"d":"-108.58"},{"v":43.4874696151163,"d":"43.49"},{"v":25.7672702179738,"d":"25.77"},{"$f":"IMAGINARY(AW36)","v":{"v":-315.897920643178,"d":"-315.90"}},{"v":-327.662744545319,"d":"-327.66"},{"v":-32.224586551915,"d":"-32.22"},{"v":37.6817916223431,"d":"37.68"},{"v":-238.937642045449,"d":"-238.94"},{"v":-17.5287579654926,"d":"-17.53"},{"v":-78.9374433166363,"d":"-78.94"},{"v":-64.6311155257107,"d":"-64.63"},{"v":-58.9184465101612,"d":"-58.92"},{"v":-2.62155773675925,"d":"-2.62"},{"v":-152.207882420422,"d":"-152.21"},{"v":-67.5841504727531,"d":"-67.58"},{"v":23.7377908030267,"d":"23.74"},{"v":24.6649178207911,"d":"24.66"},{"v":5.19943351381336,"d":"5.20"},{"v":-50.6529382834762,"d":"-50.65"},{"v":-57.5274460410629,"d":"-57.53"}]
[{"$nulls":15},"Reflection/Absorption (abs + air gap)"]
[{"$nulls":15},"Intermediate term (za + air/rc)*cos(y)",{"$f":"IMPRODUCT(IMDIV(Q36,airImpedance),COS(porousAbsAngle*PI()/180))","v":"1.03073280030353-6.50636327215335j"},"1.02263463295375-5.76472482512925j","1.01362366215499-5.10333853728176j","1.00407832123603-4.51309972116471j","0.994338233330068-3.98589426025476j","0.984712608271181-3.51448569272441j","0.975488641381947-3.0924141278914j","0.966940258664656-2.71390549142032j","0.959337656830773-2.37378968661202j","0.952958251168814-2.06742630758179j","0.948099906608431-1.79063653429102j","0.945097752012767-1.53963975999033j","0.944346580021278-1.31099331697179j","0.946332027419121-1.10153332505439j","0.951675821027361-0.908314106176929j","0.961204172581206-0.728542659530524j","0.976055606073567-0.559503194676933j","0.997858828749799-0.398464501567579j","1.02904142649971-0.242560203087013j","1.07339803624842-0.0886310592101836j","1.13721170783723+0.066967753825713j","1.23166219362675+0.228499752154282j","1.37855938994661+0.400323497082268j","1.62575549978515+0.582188670080191j","2.09319920262119+0.736465883541982j","3.06799822055486+0.531001332501201j","3.60423317783823-1.63446189282044j","1.15578425401709-2.03515963934691j","0.598895848256573-0.916343122761844j","0.728189934388726-0.262603290933293j","1.08867672999888+0.105176224808189j","1.67280308401871+0.0623191974406561j",{"$f":"IMPRODUCT(IMDIV(AW36,airImpedance),COS(porousAbsAngle*PI()/180))","v":"1.75965023773941-0.764012047885566j"},"0.86921858182438-0.792465755919437j","0.722058133743961-0.0779364812331377j","1.48101054237797+0.0911349550094142j","1.10756163064851-0.57788046481728j","0.812482633983885-0.0423940184311424j","1.55703393691304-0.190913436848216j","0.871481391739538-0.156312997658832j","1.46744608440729-0.142496673877478j","0.937272151650562-0.00634034466271166j","1.03845389271915-0.368120992109048j","1.26597570586856-0.163455033518941j","1.17841853840758+0.0574108184275927j","1.10123258342935+0.0596531130588775j","1.14293096901928+0.0125750427183737j","1.16410813706531-0.122506203999655j","0.98138602636333-0.139132482322049j"]
[{"$nulls":14},"Eq 1.22","Overall reflection factor",{"$f":"IMDIV(IMSUB(Q40,1),IMSUM(Q40,1))","v":"0.912575130031794-0.280104779392395j"},"0.89161487329413-0.308909192207228j","0.866198826760572-0.339106406306089j","0.835626187026685-0.370162883174702j","0.799208202088775-0.401303480736171j","0.756337866271128-0.431471578948026j","0.706586932538826-0.459306470367832j","0.649827973595235-0.483153355174522j","0.586370665354014-0.501122940826344j","0.517090399092337-0.511214211825989j","0.443517082393249-0.511502844179232j","0.36784833617324-0.500378880683283j","0.292860364803697-0.476795312849048j","0.221713754343064-0.440473785533598j","0.157684477506058-0.39201544779619j","0.103878883621782-0.332888574537548j","0.0630010615062261-0.26530321205781j","0.037226081928867-0.192021189818774j","0.0282006927723369-0.116173003785142j","0.0371592627269634-0.0411583270087552j","0.0651191651199099+0.0292937145052338j","0.11310495717321+0.0908091278561478j","0.182317065579116+0.137620146545597j","0.274004954753067+0.16096932479498j","0.388107092882963+0.14568678605993j","0.516594179253342+0.0630996182983337j","0.614231213886741-0.13694449346672j","0.509451484184891-0.463100395444546j","0.0584075499560066-0.539636003797937j","-0.131162065732146-0.17188323755932j","0.0448778126138443+0.048095592992923j","0.252128476358618+0.0174374062274635j",{"$f":"IMDIV(IMSUB(AW40,1),IMSUM(AW40,1))","v":"0.32686399606256-0.186358405076373j"},"0.0930482219133024-0.384507319471683j","-0.159026984132153-0.0524549566750842j","0.194963110393139+0.0295714183644379j","0.117392494412747-0.242005561385666j","-0.102855483442547-0.0257958199517653j","0.222179679767461-0.0580736721723941j","-0.061268501924976-0.0886410421118835j","0.192139636068323-0.046654480332998j","-0.0323684133966558-0.00337875685367941j","0.0498506540393592-0.171585887292367j","0.121946854203516-0.0633379281189438j","0.0825400056501725+0.0241790676224696j","0.0489442352830481+0.0270000748633761j","0.0667309582575372+0.00547656375184971j","0.0787837873716839-0.0521483651113079j","-0.00444170244759633-0.0705316710372786j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-IMABS(Q41)^2","v":{"v":0.08874794460899227,"d":"0.09"}},{"v":0.10959802869057,"d":"0.11"},{"v":0.13470643772077806,"d":"0.13"},{"v":0.16470831547503573,"d":"0.16"},{"v":0.20022176606306152,"d":"0.20"},{"v":0.24178530860453473,"d":"0.24"},{"v":0.2897724730436164,"d":"0.29"},{"v":0.34428644011671283,"d":"0.34"},{"v":0.4050452409898473,"d":"0.41"},{"v":0.47127754879366046,"d":"0.47"},{"v":0.5416574380219363,"d":"0.54"},{"v":0.614308577340724,"d":"0.61"},{"v":0.6868990363722239,"d":"0.69"},{"v":0.7568258553928054,"d":"0.76"},{"v":0.8214594942427941,"d":"0.82"},{"v":0.8783943744798517,"d":"0.88"},{"v":0.9256450719208974,"d":"0.93"},{"v":0.9617420814848077,"d":"0.96"},{"v":0.9857085541186976,"d":"0.99"},{"v":0.9969251813114289,"d":"1.00"},{"v":0.9949013726245718,"d":"0.99"},{"v":0.9789609709608521,"d":"0.98"},{"v":0.9478211828633887,"d":"0.95"},{"v":0.8990101612458179,"d":"0.90"},{"v":0.8281482448214633,"d":"0.83"},{"v":0.7291488921321706,"d":"0.73"},{"v":0.6039662215963643,"d":"0.60"},{"v":0.5259972090009168,"d":"0.53"},{"v":0.7053815415131295,"d":"0.71"},{"v":0.9532526651590025,"d":"0.95"},{"v":0.9956727958696557,"d":"1.00"},{"v":0.9361271682731402,"d":"0.94"},{"$f":"1-IMABS(AW41)^2","v":{"v":0.8584304729354053,"d":"0.86"}},{"v":0.8434961496714739,"d":"0.84"},{"v":0.971958895838047,"d":"0.97"},{"v":0.9611149168017481,"d":"0.96"},{"v":0.9276523105139618,"d":"0.93"},{"v":0.988755325198816,"d":"0.99"},{"v":0.9472636384988418,"d":"0.95"},{"v":0.9883889363251885,"d":"0.99"},{"v":0.9609057197163903,"d":"0.96"},{"v":0.9989408698163069,"d":"1.00"},{"v":0.9680731955739392,"d":"0.97"},{"v":0.9811172716114659,"d":"0.98"},{"v":0.9926025201561776,"d":"0.99"},{"v":0.9968754577899297,"d":"1.00"},{"v":0.9955169864595027,"d":"1.00"},{"v":0.991073662863591,"d":"0.99"},{"v":0.9950055546600561,"d":"1.00"}]

{"sheet":"Perforated Panel","index":1,"n_rows":55,"n_cols":65,"rows_kept":55}
[]
[null,"Perforated Panel with Porous Absorber",{"$nulls":13},"Cox & D'Antonio Appendix B.4"]
[null,"Properties of panel",{"$nulls":4},"Display options",{"$nulls":8},"Perforated Absorber"]
[null,"Panel thickness (tp)",{"v":4,"d":"4.0"},"mm",{"$f":"panel_thickness_mm/25.4","v":{"v":0.15748031496062992,"d":"0.157"}},"in","Start graph at",62.5,"Hz",{"$nulls":5},"Eq 6.8","End correction (d)",{"$f":"0.8*(1-1.47*SQRT(porosity)+0.47*SQRT(porosity^3))","v":{"v":0.07644163860899177,"d":"0.0764"}}]
[null,"Repeat distance (D)",{"v":30,"d":"30.0"},"mm",{"$f":"repeat_distance_mm/25.4","v":{"v":1.1811023622047245,"d":"1.181"}},"in",{"$nulls":4},"To see the graph in the standard",{"$nulls":4},"Panel thickness (tp)",{"$f":"panel_thickness_mm/1000","v":{"v":0.004,"d":"0.0040"}},"m",null,null,"End corrected panel thickness (t')",{"$f":"panel_thickness+2*hole_radius*delta","v":{"v":5.9416176206683905E-3,"d":"0.0059"}},"m"]
[null,"Hole radius (a)",12.7,"mm",{"$f":"hole_radius_mm/25.4","v":{"v":0.5,"d":"0.500"}},"in",{"$nulls":4},"analysis frequencies, select",{"$nulls":4},"Repeat distance (D)",{"$f":"repeat_distance_mm/1000","v":{"v":0.03,"d":"0.0300"}},"m"]
[null,"Open Area (e)",{"$f":"(PI()*hole_radius^2)/(repeat_distance^2)","v":{"v":0.5630083101083307,"d":"56.30%"}},{"$nulls":3},"Show subdivisions of",{"$nulls":3},"\"Whole Octaves\" and set the",{"$nulls":4},"Hole radius (a)",{"$f":"hole_radius_mm/1000","v":0.0127},"m"]
[null,"Properties of cavity",{"$nulls":8},"starting frequency to 62.5Hz",{"$nulls":4},"Cavity depth (d)",{"$f":"cavity_depth_mm/1000","v":{"v":0.13,"d":"0.1300"}},"m"]
[null,"Cavity depth (d)",{"v":130,"d":"130.0"},"mm",{"$f":"cavity_depth_mm/25.4","v":{"v":5.118110236220473,"d":"5.118"}},"in",{"$nulls":9},"Absorber thickness (ta)",{"$f":"absorber_thickness_mm/1000","v":{"v":0.03,"d":"0.0300"}},"m"]
[null,"Absorber thickness (ta)",{"v":30,"d":"30.0"},"mm",{"$f":"absorber_thickness_mm/25.4","v":{"v":1.1811023622047245,"d":"1.181"}},"in",{"$nulls":9},"Cavity air gap (d - ta)",{"$f":"airGap_mm/1000","v":{"v":0.1,"d":"0.1000"}},"m"]
[null,"Air space in cavity (d - ta)",{"$f":"cavity_depth_mm-absorber_thickness_mm","v":{"v":100,"d":"100.0"}},"mm",{"$f":"airGap_mm/25.4","v":{"v":3.937007874015748,"d":"3.937"}},"in","This is ignored for the \"No Air Gap\" plot.  Cavity assumed to be filled with absorber.",{"$nulls":8},"Octave subdivisions",6]
[null,"Absorber flow resisitivity",{"v":16500,"d":"16,500"},"rayls/m"]
[{"$nulls":15},"Interval number",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]
[null,"This plot is a simplification of reality because it is only calculated for normal incident sound.",{"$nulls":13},"Angular values",{"$f":"start_freq_perf","v":62.5},{"$f":"POWER(2,LOG(start_freq_perf,2)+R13/subdiv_perf)","v":{"v":70.15387801933585,"d":"70"}},{"v":78.74506561842958,"d":"79"},{"v":88.38834764831847,"d":"88"},{"v":99.21256574801254,"d":"99"},{"v":111.36233976754242,"d":"111"},{"v":125.00000000000004,"d":"125"},{"v":140.30775603867173,"d":"140"},{"v":157.49013123685916,"d":"157"},{"v":176.77669529663694,"d":"177"},{"v":198.42513149602507,"d":"198"},{"v":222.72467953508487,"d":"223"},{"v":250.0000000000001,"d":"250"},{"v":280.61551207734345,"d":"281"},{"v":314.98026247371837,"d":"315"},{"v":353.5533905932743,"d":"354"},{"v":396.8502629920502,"d":"397"},{"v":445.44935907016975,"d":"445"},{"v":500.0000000000003,"d":"500"},{"v":561.231024154687,"d":"561"},{"v":629.9605249474367,"d":"630"},{"v":707.106781186548,"d":"707"},{"v":793.7005259841005,"d":"794"},{"v":890.8987181403396,"d":"891"},{"v":1000.0000000000007,"d":"1,000"},{"v":1122.462048309374,"d":"1,122"},{"v":1259.9210498948737,"d":"1,260"},{"v":1414.213562373096,"d":"1,414"},{"v":1587.4010519681997,"d":"1,587"},{"v":1781.7974362806794,"d":"1,782"},{"v":2000.0000000000016,"d":"2,000"},{"v":2244.9240966187463,"d":"2,245"},{"v":2519.8420997897474,"d":"2,520"},{"v":2828.4271247461925,"d":"2,828"},{"v":3174.8021039364025,"d":"3,175"},{"v":3563.5948725613557,"d":"3,564"},{"v":4000.000000000007,"d":"4,000"},{"v":4489.848193237493,"d":"4,490"},{"v":5039.684199579496,"d":"5,040"},{"v":5656.854249492385,"d":"5,657"},{"v":6349.604207872805,"d":"6,350"},{"v":7127.189745122712,"d":"7,127"},{"v":8000,"d":"8,000"},{"v":8979.696386474987,"d":"8,980"},{"v":10079.368399158991,"d":"10,079"},{"v":11313.708498984772,"d":"11,314"},{"v":12699.208415745612,"d":"12,699"},{"v":14254.379490245426,"d":"14,254"},{"v":16000.000000000002,"d":"16,000"}]
[{"$nulls":14},"2pf","Angular frequency (w)",{"$f":"2*PI()*Q14","v":{"v":392.6990816987241,"d":"392.7"}},{"v":440.7898156127599,"d":"440.8"},{"v":494.76983930660913,"d":"494.8"},{"v":555.3603672697959,"d":"555.4"},{"v":623.3709353955011,"d":"623.4"},{"v":699.7102170005635,"d":"699.7"},{"v":785.3981633974486,"d":"785.4"},{"v":881.5796312255201,"d":"881.6"},{"v":989.5396786132183,"d":"989.5"},{"v":1110.7207345395918,"d":"1110.7"},{"v":1246.7418707910022,"d":"1246.7"},{"v":1399.4204340011272,"d":"1399.4"},{"v":1570.7963267948974,"d":"1570.8"},{"v":1763.1592624510401,"d":"1763.2"},{"v":1979.0793572264367,"d":"1979.1"},{"v":2221.4414690791864,"d":"2221.4"},{"v":2493.4837415820048,"d":"2493.5"},{"v":2798.8408680022544,"d":"2798.8"},{"v":3141.5926535897947,"d":"3141.6"},{"v":3526.3185249020808,"d":"3526.3"},{"v":3958.1587144528735,"d":"3958.2"},{"v":4442.882938158369,"d":"4442.9"},{"v":4986.9674831640095,"d":"4987.0"},{"v":5597.68173600451,"d":"5597.7"},{"v":6283.18530717959,"d":"6283.2"},{"v":7052.6370498041615,"d":"7052.6"},{"v":7916.317428905749,"d":"7916.3"},{"v":8885.765876316738,"d":"8885.8"},{"v":9973.934966328012,"d":"9973.9"},{"v":11195.36347200902,"d":"11195.4"},{"v":12566.370614359183,"d":"12566.4"},{"v":14105.274099608312,"d":"14105.3"},{"$f":"2*PI()*AW14","v":{"v":15832.634857811498,"d":"15832.6"}},{"v":17771.53175263348,"d":"17771.5"},{"v":19947.86993265604,"d":"19947.9"},{"v":22390.72694401802,"d":"22390.7"},{"v":25132.741228718387,"d":"25132.7"},{"v":28210.54819921663,"d":"28210.5"},{"v":31665.269715623002,"d":"31665.3"},{"v":35543.06350526696,"d":"35543.1"},{"v":39895.73986531208,"d":"39895.7"},{"v":44781.45388803605,"d":"44781.5"},{"v":50265.48245743669,"d":"50265.5"},{"v":56421.09639843326,"d":"56421.1"},{"v":63330.539431246005,"d":"63330.5"},{"v":71086.12701053394,"d":"71086.1"},{"v":79791.47973062418,"d":"79791.5"},{"v":89562.9077760721,"d":"89562.9"},{"v":100530.96491487339,"d":"100531.0"}]
[{"$nulls":14},"2p/l","Wave number (kair)",{"$f":"TwoPiByC*Q14","v":{"v":1.1436219656127162,"d":"1.1436"}},{"v":1.2836722540132413,"d":"1.2837"},{"v":1.4408733875976119,"d":"1.4409"},{"v":1.617325693997281,"d":"1.6173"},{"v":1.815386711267567,"d":"1.8154"},{"v":2.037702686403008,"d":"2.0377"},{"v":2.287243931225433,"d":"2.2872"},{"v":2.5673445080264834,"d":"2.5673"},{"v":2.8817467751952237,"d":"2.8817"},{"v":3.234651387994562,"d":"3.2347"},{"v":3.630773422535134,"d":"3.6308"},{"v":4.075405372806017,"d":"4.0754"},{"v":4.574487862450867,"d":"4.5745"},{"v":5.134689016052967,"d":"5.1347"},{"v":5.763493550390449,"d":"5.7635"},{"v":6.4693027759891315,"d":"6.4693"},{"v":7.261546845070269,"d":"7.2615"},{"v":8.150810745612034,"d":"8.1508"},{"v":9.148975724901735,"d":"9.1490"},{"v":10.269378032105935,"d":"10.2694"},{"v":11.526987100780898,"d":"11.5270"},{"v":12.938605551978252,"d":"12.9386"},{"v":14.52309369014054,"d":"14.5231"},{"v":16.30162149122407,"d":"16.3016"},{"v":18.29795144980347,"d":"18.2980"},{"v":20.53875606421187,"d":"20.5388"},{"v":23.0539742015618,"d":"23.0540"},{"v":25.877211103956505,"d":"25.8772"},{"v":29.046187380281054,"d":"29.0462"},{"v":32.603242982448144,"d":"32.6032"},{"v":36.59590289960695,"d":"36.5959"},{"v":41.077512128423706,"d":"41.0775"},{"$f":"TwoPiByC*AW14","v":{"v":46.1079484031236,"d":"46.1079"}},{"v":51.75442220791302,"d":"51.7544"},{"v":58.092374760562166,"d":"58.0924"},{"v":65.20648596489623,"d":"65.2065"},{"v":73.19180579921395,"d":"73.1918"},{"v":82.15502425684743,"d":"82.1550"},{"v":92.21589680624722,"d":"92.2159"},{"v":103.50884441582603,"d":"103.5088"},{"v":116.18474952112433,"d":"116.1847"},{"v":130.41297192979246,"d":"130.4130"},{"v":146.38361159842768,"d":"146.3836"},{"v":164.31004851369485,"d":"164.3100"},{"v":184.43179361249443,"d":"184.4318"},{"v":207.01768883165212,"d":"207.0177"},{"v":232.3694990422487,"d":"232.3695"},{"v":260.825943859585,"d":"260.8259"},{"v":292.76722319685535,"d":"292.7672"}]
[{"$nulls":15},"Boundary layer values"]
[{"$nulls":14},"Eq 5.19","Viscous boundary layer (mm)",{"$f":"1000*SQRT((2*airViscosity)/(airDensity*Q15))","v":{"v":0.2797282561013913,"d":"0.28"}},{"v":0.2640283154653494,"d":"0.26"},{"v":0.24920954478836208,"d":"0.25"},{"v":0.23522248780083294,"d":"0.24"},{"v":0.22202046400028913,"d":"0.22"},{"v":0.20955941285954366,"d":"0.21"},{"v":0.197797746778781,"d":"0.20"},{"v":0.1866962122908095,"d":"0.19"},{"v":0.17621775905626344,"d":"0.18"},{"v":0.16632741621153888,"d":"0.17"},{"v":0.1569921756567882,"d":"0.16"},{"v":0.1481808818944547,"d":"0.15"},{"v":0.1398641280506956,"d":"0.14"},{"v":0.13201415773267466,"d":"0.13"},{"v":0.12460477239418101,"d":"0.12"},{"v":0.11761124390041638,"d":"0.12"},{"v":0.11101023200014455,"d":"0.11"},{"v":0.10477970642977183,"d":"0.10"},{"v":0.09889887338939049,"d":"0.10"},{"v":0.09334810614540474,"d":"0.09"},{"v":0.0881088795281317,"d":"0.09"},{"v":0.08316370810576944,"d":"0.08"},{"v":0.0784960878283941,"d":"0.08"},{"v":0.07409044094722735,"d":"0.07"},{"v":0.0699320640253478,"d":"0.07"},{"v":0.06600707886633733,"d":"0.07"},{"v":0.062302386197090505,"d":"0.06"},{"v":0.05880562195020822,"d":"0.06"},{"v":0.0555051160000723,"d":"0.06"},{"v":0.05238985321488591,"d":"0.05"},{"v":0.04944943669469524,"d":"0.05"},{"v":0.04667405307270239,"d":"0.05"},{"$f":"1000*SQRT((2*airViscosity)/(airDensity*AW15))","v":{"v":0.044054439764065846,"d":"0.04"}},{"v":0.04158185405288472,"d":"0.04"},{"v":0.03924804391419705,"d":"0.04"},{"v":0.037045220473613694,"d":"0.04"},{"v":0.034966032012673884,"d":"0.03"},{"v":0.03300353943316867,"d":"0.03"},{"v":0.031151193098545246,"d":"0.03"},{"v":0.029402810975104107,"d":"0.03"},{"v":0.027752558000036138,"d":"0.03"},{"v":0.026194926607442964,"d":"0.03"},{"v":0.02472471834734763,"d":"0.02"},{"v":0.023337026536351193,"d":"0.02"},{"v":0.022027219882032923,"d":"0.02"},{"v":0.020790927026442356,"d":"0.02"},{"v":0.01962402195709852,"d":"0.02"},{"v":0.018522610236806843,"d":"0.02"},{"v":0.017483016006336956,"d":"0.02"}]
[{"$nulls":14},"Eq 5.20","Thermal boundary layer (mm)",{"$f":"1000*SQRT((2*airThermalConductivity)/(airDensity*airSpecificHeatCapacity*Q15))","v":{"v":10.046118764039223,"d":"10.05"}},{"v":9.482273443526182,"d":"9.48"},{"v":8.950074329168151,"d":"8.95"},{"v":8.447745255893658,"d":"8.45"},{"v":7.973609747116662,"d":"7.97"},{"v":7.526085419651793,"d":"7.53"},{"v":7.103678702657549,"d":"7.10"},{"v":6.704979852982478,"d":"6.70"},{"v":6.3286582502784405,"d":"6.33"},{"v":5.973457956178892,"d":"5.97"},{"v":5.638193522721343,"d":"5.64"},{"v":5.321746036024986,"d":"5.32"},{"v":5.02305938201961,"d":"5.02"},{"v":4.74113672176309,"d":"4.74"},{"v":4.475037164584076,"d":"4.48"},{"v":4.223872627946825,"d":"4.22"},{"v":3.98680487355833,"d":"3.99"},{"v":3.7630427098258963,"d":"3.76"},{"v":3.5518393513287747,"d":"3.55"},{"v":3.3524899264912387,"d":"3.35"},{"v":3.1643291251392203,"d":"3.16"},{"v":2.9867289780894453,"d":"2.99"},{"v":2.8190967613606714,"d":"2.82"},{"v":2.660873018012493,"d":"2.66"},{"v":2.511529691009805,"d":"2.51"},{"v":2.370568360881545,"d":"2.37"},{"v":2.2375185822920374,"d":"2.24"},{"v":2.111936313973414,"d":"2.11"},{"v":1.9934024367791658,"d":"1.99"},{"v":1.881521354912948,"d":"1.88"},{"v":1.775919675664387,"d":"1.78"},{"v":1.67624496324562,"d":"1.68"},{"$f":"1000*SQRT((2*airThermalConductivity)/(airDensity*airSpecificHeatCapacity*AW15))","v":{"v":1.58216456256961,"d":"1.58"}},{"v":1.4933644890447226,"d":"1.49"},{"v":1.4095483806803357,"d":"1.41"},{"v":1.3304365090062469,"d":"1.33"},{"v":1.2557648455049017,"d":"1.26"},{"v":1.1852841804407728,"d":"1.19"},{"v":1.1187592911460187,"d":"1.12"},{"v":1.0559681569867068,"d":"1.06"},{"v":0.9967012183895825,"d":"1.00"},{"v":0.9407606774564743,"d":"0.94"},{"v":0.8879598378321939,"d":"0.89"},{"v":0.8381224816228099,"d":"0.84"},{"v":0.7910822812848048,"d":"0.79"},{"v":0.7466822445223611,"d":"0.75"},{"v":0.7047741903401677,"d":"0.70"},{"v":0.6652182545031233,"d":"0.67"},{"v":0.6278824227524513,"d":"0.63"}]
[{"$nulls":15},"Properties of porous absorber"]
[{"$nulls":14},"Eq 5.11","Delany & Bazley's term",{"$f":"(airDensity*Q14)/sigma","v":{"v":0.004561054228691726,"d":"0.005"}},{"v":0.005119610271987445,"d":"0.005"},{"v":0.00574656823244073,"d":"0.006"},{"v":0.006450304748934998,"d":"0.006"},{"v":7.2402222807092555E-3,"d":"0.007"},{"v":0.008126874731420066,"d":"0.008"},{"v":0.009122108457383456,"d":"0.009"},{"v":0.010239220543974891,"d":"0.010"},{"v":0.01149313646488146,"d":"0.011"},{"v":0.012900609497869996,"d":"0.013"},{"v":0.014480444561418511,"d":"0.014"},{"v":0.016253749462840132,"d":"0.016"},{"v":0.018244216914766912,"d":"0.018"},{"v":0.020478441087949783,"d":"0.020"},{"v":0.02298627292976293,"d":"0.023"},{"v":0.02580121899574002,"d":"0.026"},{"v":0.028960889122837025,"d":"0.029"},{"v":0.032507498925680264,"d":"0.033"},{"v":0.03648843382953383,"d":"0.036"},{"v":0.04095688217589957,"d":"0.041"},{"v":0.04597254585952586,"d":"0.046"},{"v":0.051602437991479996,"d":"0.052"},{"v":0.05792177824567406,"d":"0.058"},{"v":0.06501499785136054,"d":"0.065"},{"v":0.07297686765906766,"d":"0.073"},{"v":0.08191376435179915,"d":"0.082"},{"v":0.09194509171905173,"d":"0.092"},{"v":0.10320487598295999,"d":"0.103"},{"v":0.11584355649134802,"d":"0.116"},{"v":0.13002999570272109,"d":"0.130"},{"v":0.14595373531813535,"d":"0.146"},{"v":0.16382752870359815,"d":"0.164"},{"$f":"(airDensity*AW14)/sigma","v":{"v":0.18389018343810346,"d":"0.184"}},{"v":0.20640975196592,"d":"0.206"},{"v":0.23168711298269626,"d":"0.232"},{"v":0.26005999140544195,"d":"0.260"},{"v":0.291907470636271,"d":"0.292"},{"v":0.32765505740719636,"d":"0.328"},{"v":0.36778036687620697,"d":"0.368"},{"v":0.41281950393184,"d":"0.413"},{"v":0.4633742259653925,"d":"0.463"},{"v":0.520119982810884,"d":"0.520"},{"v":0.583814941272541,"d":"0.584"},{"v":0.6553101148143927,"d":"0.655"},{"v":0.7355607337524139,"d":"0.736"},{"v":0.8256390078636803,"d":"0.826"},{"v":0.9267484519307851,"d":"0.927"},{"v":1.040239965621768,"d":"1.040"},{"v":1.167629882545082,"d":"1.168"}]
[{"$nulls":14},"Eq 5.9","Characteristic impedance (zc)",{"$f":"IMPRODUCT(airImpedance,COMPLEX(1+0.0571*(Q21^-0.754),-0.087*(Q21^-0.732),\"j\"))","v":"1787.98109383187-1860.07330550798j"},"1673.3201246607-1709.24532464674j","1568.22412821793-1570.64754984422j","1471.89519825913-1443.28826895666j","1383.60198956339-1326.25618491845j","1302.67416543908-1218.71389511534j","1228.49730841642-1119.89189949642j","1160.50825548811-1029.08309455108j","1098.19082248235-945.637713753479j","1041.07188510691-868.958678271748j","988.717786911013-798.497324674833j","940.73104689361-733.74947906726j","896.747341761659-674.251849560947j","856.432739927211-619.578711271131j","819.481166243412-569.338860116388j","785.61207823117-523.172813626225j","754.568336154121-480.750238727125j","726.114250771071-441.767588101985j","700.033793944169-405.945928210378j","676.128958517446-373.028943428378j","654.218255013611-342.781102026914j","634.135333735836-314.985970865678j","615.727721813263-289.444666743628j","598.855665601647-265.97443332502j","583.391069650505-244.407333458401j","569.216524181213-224.589047531685j","556.224413692467-206.377769265153j","544.316099925549-189.643191041416j","533.401172986293-174.265571512036j","523.396764938175-160.13487880925j","514.226920655183-147.150003232176j","505.822021157885-135.21803377403j",{"$f":"IMPRODUCT(airImpedance,COMPLEX(1+0.0571*(AW21^-0.754),-0.087*(AW21^-0.732),\"j\"))","v":"498.118255054607-124.253593313662j"},"491.057134074744-114.17822771449j","484.58504901611-104.91984445965j","478.652862734964-96.4121968065901j","473.215537088693-88.5944097700933j","468.231790998726-81.4105445419609j","463.663787037752-74.8091982306532j","459.476844161694-68.743136056885j","455.639174405466-63.168953373425j","452.12164154346-58.0467650907279j","448.897539882491-53.3399202861517j","445.942391507755-49.0147399546903j","443.233760442414-45.0402760247403j","440.751082309951-41.3880899145865j","438.475508206022-38.0320490451027j","436.389761594417-34.948139852652j","434.47800714076-32.1142959642295j"]
[{"$nulls":14},"Eq 5.10","Wavenumber (ka)",{"$f":"IMPRODUCT(Q16,COMPLEX(1+0.0978*(Q21^-0.7),-0.189*(Q21^-0.595),\"j\"))","v":"6.01078257968505-5.3407282086255j"},"6.32247291646459-5.59654502218689j","6.65736697166219-5.86461526628144j","7.01777852702292-6.14552587089911j","7.40628610215882-6.43989187952947j","7.82576471851884-6.74835779577672j","8.27942153009301-7.07159899447689j","8.77083579356213-7.41032320040622j","9.30400370846593-7.76527203781878j","9.88338872290681-8.13722265420555j","10.5139779732044-8.52698942183033j","11.2013456077393-8.93542572076827j","11.9517238370672-9.36342580735008j","12.772082655474-9.81192677210361j","13.6702192948523-10.2819105914794j","14.6548586016642-10.7744062778518j","15.7357656735371-11.2904921325044j","16.9238722556799-11.8312981065311j","18.2314185809778-12.3980082748223j","19.6721125437952-12.9918634285541j","21.2613083289255-13.6141637918548j","23.016206876881-14.266271868598j","24.9560808582697-14.9496154255556j","27.1025271572753-15.6656906184399j","29.479750231586-16.4160652676826j","32.1148801284436-17.20238229112j","35.0383293992969-18.0263633011014j","38.2841936750277-18.8898123738965j","41.8907012468224-19.7946199996541j","45.9007176522728-20.7427672215615j","50.3623120009455-21.7363299732656j","55.3293925982901-22.7774836240542j",{"$f":"IMPRODUCT(AW16,COMPLEX(1+0.0978*(AW21^-0.7),-0.189*(AW21^-0.595),\"j\"))","v":"60.8624203523565-23.868507741747j"},"67.0292094867553-25.0117910837261j","73.905826249486-26.2098368270329j","81.5775976162465-27.4652680489826j","90.1402434561478-28.7808334702961j","99.7011472769831-30.1594134733229j","110.380782518399-31.6040264085338j","122.314313439204-33.1178352030882j","135.653391977414-34.7041542859472j","150.568174579598-36.3664568446949j","167.249585934686-38.1083824299556j","185.911859845798-39.9337449240564j","206.795391176059-41.8465408913829j","230.169936960115-43.8509583287115j","256.338209437718-45.9513858346736j","285.639909001728-48.1524222184333j","318.456250929939-50.4588865686111j"]
[{"$nulls":15},"Intermediate values"]
[{"$nulls":15},"kair * tair",{"$f":"Q16*airGap","v":0.11436219656127163},0.12836722540132414,0.14408733875976118,0.16173256939972813,0.1815386711267567,0.20377026864030082,0.2287243931225433,0.25673445080264834,0.28817467751952236,0.32346513879945626,0.3630773422535134,0.40754053728060174,0.45744878624508667,0.5134689016052967,0.5763493550390449,0.6469302775989132,0.7261546845070269,0.8150810745612035,0.9148975724901736,1.0269378032105936,1.1526987100780899,1.2938605551978253,1.452309369014054,1.630162149122407,1.8297951449803471,2.053875606421187,2.30539742015618,2.5877211103956506,2.9046187380281054,3.2603242982448144,3.659590289960695,4.107751212842371,{"$f":"AW16*airGap","v":4.61079484031236},5.175442220791302,5.809237476056217,6.5206485964896235,7.319180579921396,8.215502425684743,9.221589680624723,10.350884441582604,11.618474952112434,13.041297192979247,14.638361159842768,16.431004851369487,18.443179361249445,20.701768883165215,23.236949904224872,26.0825943859585,29.276722319685536]
[{"$nulls":15},"cot(kair * tair)",{"$f":"COS(Q25)/SIN(Q25)","v":8.70599423024322},{"$f":"COS(R25)/SIN(R25)","v":7.747314305268111},6.892139338227932,6.129041414985806,5.447821955607797,4.839375081088989,4.29556542073074,3.8091186583509447,3.3735232542110203,2.982941882005205,2.632131179551623,2.316368415322341,2.031383598484321,1.7732953689667712,1.5385486277210014,1.3238511817923115,1.1261054525743008,0.9423290799998737,0.7695541419463814,0.6046867609112845,0.4442927104251694,0.28423963428956217,0.11904457513488516,-0.05943566178951344,-0.26494979390389745,-0.5245310152173872,-0.9032378526928779,-1.6169592826074977,-4.140585104419652,8.38274002598429,1.754675089589875,0.6909669714903396,0.10194511939114778,-0.49925725990048836,-1.949536671726612,4.131723644567343,0.5923845053596543,-0.3781401035583194,-4.853627120859815,0.7518590601830144,-0.7182971408089581,1.944846952216688,-0.5478541318494531,1.1331911823374339,-2.3237978182747034,-0.2890887246307247,0.3369421859040994,0.715333837548285,0.638724625342242]
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[{"$nulls":15},"cot(ka * ta)",{"$f":"IMDIV(IMCOS(Q27),IMSIN(Q27))","v":"3.03907399109389+2.80720189557854j"},"2.89299797354295+2.6728767405205j","2.75287700140115+2.54249604516655j","2.61838306790678+2.41601479241177j","2.48919347487008+2.29339506127762j","2.36499070003231+2.17460638565336j","2.24546234844792+2.0596261076479j","2.13030118810419+1.94843971432763j","2.01920526542579+1.84104114521935j","1.91187809010966+1.73743305742253j","1.80802887064404+1.63762703609362j","1.70737277166343+1.54164374123808j","1.60963115182829+1.4495129882138j","1.51453172613927+1.361273770456j","1.42180857957188+1.27697425039322j","1.33120193986597+1.19667177054577j","1.24245759658797+1.12043297430411j","1.15532583170836+1.04833417888107j","1.06955970455723+0.980462217226042j","0.984912512039644+0.91691607013004j","0.901134224937357+0.857809758495879j","0.817966686209321+0.803277182240787j","0.735137355047668+0.753479916361226j","0.652351409514784+0.708619475153236j","0.56928212529094+0.668956353044938j","0.485559734003626+0.634839458602128j","0.400759682153503+0.606751758656984j","0.314392958558663+0.585381725343696j","0.225905384595088+0.571736736516889j","0.134703063887979+0.56732593736716j","0.0402467069569703+0.574459027472215j","-0.0576780339835567+0.596734992139401j",{"$f":"IMDIV(IMCOS(AW27),IMSIN(AW27))","v":"-0.158242498507541+0.639814160397264j"},"-0.25772486424072+0.712465327096894j","-0.344932111066093+0.827110607350575j","-0.391333559194368+0.995546749754697j","-0.339675318323662+1.20508493420894j","-0.136002051414263+1.36284772252403j","0.135290911767865+1.32190936264031j","0.270009219875248+1.11031594453491j","0.220347203643135+0.906768006009976j","0.0703535172381285+0.808338642051238j","-0.0989588734315179+0.84092153766009j","-0.183634382303068+1.01253296281255j","-0.030320009250783+1.17392526866831j","0.142215423652487+1.03741876731908j","0.036343575552858+0.885915251775526j","-0.108135744152546+0.978646386561306j","0.0271814291282161+1.09791847431602j"]
[{"$nulls":15},"Absorbent against panel"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":14},"Eq 5.26","At top of air layer (z1)",{"$f":"IMPRODUCT(\"-j\",airImpedance,Q26)","v":"-3599.68862019472j"},"-3203.30089869199j","-2849.7096240233j","-2534.18966872095j","-2252.52420112165j","-2000.94819127433j","-1776.097887659j","-1574.96556106197j","-1394.85886930187j","-1233.36423886607j","-1088.31368403365j","-957.754485507093j","-839.921119785756j","-733.208751475977j","-636.14744512285j","-547.375969693927j","-465.613561824942j","-389.627097841454j","-318.189423761048j","-250.021306523878j","-183.702788154532j","-117.525253279643j","-49.221650172974j","24.575007715285j","109.549436034045j","216.879115294849j","373.46395295932j","668.568089409108j","1712.01779913318j","-3466.03191772888j","-725.509779250034j","-285.695795152704j",{"$f":"IMPRODUCT(\"-j\",airImpedance,AW26)","v":"-42.1514965955192j"},"206.429114180929j","806.079671806826j","-1708.35382976391j","-244.934662983719j","156.350508812606j","2006.84101684035j","-310.872995243817j","296.996066768146j","-804.140602068745j","226.522581084922j","-468.543315753048j","960.826338825069j","119.530218463142j","-139.316305546028j","-295.770822557833j","-264.095025160426j"]
[{"$nulls":14},"Eq 5.27","At top of porous absorber (z2)",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",Q31,Q22,Q28),IMPRODUCT(Q22,Q22)),IMSUB(Q31,IMPRODUCT(\"j\",Q22,Q28)))","v":"426.179599203616-2690.20185520718j"},"422.831230242817-2383.55480175778j","419.105442218685-2110.08980385473j","415.158706880581-1866.04232422363j","411.131449031844-1648.05739936008j","407.151518415032-1453.14295178252j","403.337662379051-1278.62799477057j","399.80314177466-1122.12510775771j","396.659675493666-981.496598280443j","394.021967110494-854.823786425303j","392.013175562454-740.378845301881j","390.771867396118-636.598598237488j","390.461278484838-542.059597037293j","391.282206251961-455.453664463635j","393.491717599146-375.562843840305j","397.431428303115-301.232306326162j","403.572086649789-231.339147439898j","412.58711818732-164.7540871164j","425.480262761037-100.291957434488j","443.820498134521-36.6464997330676j","470.205692215294+27.6893201386473j","509.258364417547+94.4783485715801j","569.99630565052+165.522730515678j","672.205082730924+240.718966159413j","865.480168054931+304.508341039144j","1268.53269014864+219.554413127541j","1490.25106285076-675.804936246009j","477.884928080104-841.482408590111j","247.626923776496-378.882620866078j","301.086464203435-108.579221740634j","450.137816819833+43.4874696151152j","691.657961873077+25.7672702179738j",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",AW31,AW22,AW28),IMPRODUCT(AW22,AW22)),IMSUB(AW31,IMPRODUCT(\"j\",AW22,AW28)))","v":"727.566865862318-315.897920643178j"},"359.39792224829-327.662744545319j","298.551133669263-32.224586551915j","612.357032958594+37.6817916223431j","457.946202647364-238.937642045449j","335.939171829191-17.5287579654926j","643.790610898013-78.9374433166363j","360.333531770401-64.6311155257107j","606.748503512693-58.9184465101612j","387.536197370957-2.62155773675925j","429.372058073786-152.207882420422j","523.446055825231-67.5841504727531j","487.243580726995+23.7377908030267j","455.329316092084+24.6649178207911j","472.570449053915+5.19943351381336j","481.326624260008-50.6529382834762j","405.77606849844-57.5274460410629j"]
[{"$nulls":14},"Eq 6.15","Surface resistance (zm)",{"$f":"(airDensity/porosity)*SQRT(8*airViscosity*Q15)*(1+end_corrected_panel_thickness/(2*hole_radius))","v":{"v":0.6362134544631408,"d":"0.636"}},{"v":0.6740446751385358,"d":"0.674"},{"v":0.7141254572586789,"d":"0.714"},{"v":0.7565895667080268,"d":"0.757"},{"v":0.8015787235044446,"d":"0.802"},{"v":0.8492430747765927,"d":"0.849"},{"v":0.8997416958660113,"d":"0.900"},{"v":0.9532431212262845,"d":"0.953"},{"v":1.0099259068911117,"d":"1.010"},{"v":1.069979226388475,"d":"1.070"},{"v":1.133603502089699,"d":"1.134"},{"v":1.2010110741004858,"d":"1.201"},{"v":1.2724269089262819,"d":"1.272"},{"v":1.3480893502770719,"d":"1.348"},{"v":1.4282509145173579,"d":"1.428"},{"v":1.5131791334160545,"d":"1.513"},{"v":1.6031574470088896,"d":"1.603"},{"v":1.6984861495531853,"d":"1.698"},{"v":1.7994833917320228,"d":"1.799"},{"v":1.906486242452569,"d":"1.906"},{"v":2.0198518137822234,"d":"2.020"},{"v":2.13995845277695,"d":"2.140"},{"v":2.267207004179398,"d":"2.267"},{"v":2.402022148200972,"d":"2.402"},{"v":2.5448538178525637,"d":"2.545"},{"v":2.6961787005541438,"d":"2.696"},{"v":2.856501829034716,"d":"2.857"},{"v":3.0263582668321076,"d":"3.026"},{"v":3.206314894017778,"d":"3.206"},{"v":3.396972299106371,"d":"3.397"},{"v":3.598966783464046,"d":"3.599"},{"v":3.8129724849051367,"d":"3.813"},{"$f":"(airDensity/porosity)*SQRT(8*airViscosity*AW15)*(1+end_corrected_panel_thickness/(2*hole_radius))","v":{"v":4.039703627564449,"d":"4.040"}},{"v":4.279916905553901,"d":"4.280"},{"v":4.534414008358796,"d":"4.534"},{"v":4.804044296401942,"d":"4.804"},{"v":5.089707635705129,"d":"5.090"},{"v":5.392357401108287,"d":"5.392"},{"v":5.713003658069433,"d":"5.713"},{"v":6.052716533664215,"d":"6.053"},{"v":6.4126297880355585,"d":"6.413"},{"v":6.7939445982127395,"d":"6.794"},{"v":7.197933566928088,"d":"7.198"},{"v":7.6259449698102735,"d":"7.626"},{"v":8.079407255128897,"d":"8.079"},{"v":8.559833811107804,"d":"8.560"},{"v":9.068828016717594,"d":"9.069"},{"v":9.608088592803885,"d":"9.608"},{"v":10.179415271410253,"d":"10.179"}]
[{"$nulls":14},"Eq 6.26","Overall impedence (z3)",{"$f":"IMSUM(IMPRODUCT(IMDIV(\"j\",porosity),end_corrected_panel_thickness*Q15*airDensity),Q32,Q33)","v":"426.815812658079-2685.21164382911j"},"423.505274917956-2377.95347887286j","419.819567675944-2103.80253149608j","415.915296447289-1858.98509961366j","411.933027755348-1640.13593256899j","408.000761489809-1444.25140594258j","404.237404074917-1268.64757201444j","400.756384895886-1110.92246198787j","397.669601400557-968.922053563141j","395.091946336882-840.709337205362j","393.146779064544-724.535911719708j","391.972878470219-618.815506557612j","391.733705393764-522.098751525027j","392.630295602238-433.04837292395j","394.919968513663-350.413754405701j","398.944607436531-273.003407886281j","405.175244096798-199.653280275552j","414.285604336873-129.187903756649j","427.279746152769-60.3702664099552j","445.726984376974+8.1640833463034j","472.225544029076+77.9874990078554j","511.398322870324+150.936145451343j","572.263512654699+228.894464844371j","674.607104879125+311.851332878915j","868.025021872784+384.35172308821j","1271.22886884919+309.175579286283j","1493.10756467979-575.208578507593j","480.911286346936-728.566814830586j","250.833238670514-252.139152208693j","304.483436502541+33.68551169837j","453.736783603297+203.174233713246j","695.470934357982+205.009602535458j",{"$f":"IMSUM(IMPRODUCT(IMDIV(\"j\",porosity),end_corrected_panel_thickness*AW15*airDensity),AW32,AW33)","v":"731.606569489882-114.705205166346j"},"363.677839153844-101.831557026269j","303.085547677622+221.262350762856j","617.161077254996+322.21125850035j","463.035910283069+80.435886150814j","341.331529230299+340.955906669475j","649.503614556082+323.447987637029j","366.386248304065+387.031259512389j","613.161133300729+448.055428119381j","394.33014196917+566.437376019256j","436.569991640714+486.539173972102j","531.072000795041+649.385178797182j","495.322987982124+828.508652710356j","463.889149903192+927.989667896992j","481.639277070633+1019.14718277289j","490.934712852812+1087.46492922855j","415.95548376985+1219.96666674399j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q34,airImpedance),IMSUM(Q34,airImpedance))","v":"0.912224240535807-0.280494809303774j"},"0.891091542971857-0.309421913716339j","0.865422264166944-0.339766829559947j","0.834482144986856-0.370990810556623j","0.797539020496363-0.402303525993402j","0.753932741273453-0.432616653289141j","0.703175369110806-0.460512800506504j","0.645081330963881-0.484246089938374j","0.579918599904961-0.501793909504882j","0.508559737422665-0.510977762245395j","0.432598601909708-0.509661415058873j","0.35439066831701-0.496015135601272j","0.276979859865199-0.468809034444693j","0.203897482108663-0.427676135581759j","0.138855833360932-0.373280055297867j","0.0853965149947117-0.307341987793702j","0.0465730150123602-0.232523502199032j","0.0247375608876158-0.152208863419357j","0.0214678514439666-0.0702635662808679j","0.0376271284077208+0.0091444339587038j","0.0735185364069732+0.0815785674778235j","0.129076165819731+0.142132168858246j","0.20400866375758+0.184834500197947j","0.297686522473236+0.201288036715512j","0.40796075143036+0.17756672428343j","0.52513760740839+0.0871465197470131j","0.602452988334714-0.119938555786427j","0.444211070275981-0.452746803494943j","-0.0880770166469184-0.412982799964979j","-0.149274625094899+0.0539224003134137j","0.0960473340973046+0.211782677802562j","0.278938257064085+0.133302191627454j",{"$f":"IMDIV(IMSUB(AW34,airImpedance),IMSUM(AW34,airImpedance))","v":"0.285001879650285-0.0716230110550789j"},"-0.0461122109184862-0.137074178590618j","-0.0535933736001901+0.325333821857766j","0.269075101238542+0.228512103524019j","0.0644254051236694+0.0858563094521664j","0.0900881865120823+0.41102037440988j","0.287973697921317+0.216659138254949j","0.149177690283141+0.422249361127717j","0.323384904517668+0.295296273265832j","0.313734609423387+0.481214567652851j","0.267232647209731+0.419414386866545j","0.405505136434336+0.408722066706261j","0.503070841969984+0.453028368642076j","0.55514309555908+0.470527338824726j","0.5976880889995+0.458060201717589j","0.626152068250179+0.449517140917604j","0.684831676514481+0.463566322126326j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q36),2)","v":{"v":0.08916959693250959,"d":"0.09"}},{"v":0.11021394135615348,"d":"0.11"},{"v":0.13560280621494214,"d":"0.14"},{"v":0.16600536818067568,"d":"0.17"},{"v":0.20208338375897783,"d":"0.20"},{"v":0.24442825293279968,"d":"0.24"},{"v":0.2934723608455385,"d":"0.29"},{"v":0.34937580082126407,"d":"0.35"},{"v":0.41189728986807606,"d":"0.41"},{"v":0.48026871996327847,"d":"0.48"},{"v":0.5531036916259533,"d":"0.55"},{"v":0.6283762394642749,"d":"0.63"},{"v":0.7035002464520894,"d":"0.70"},{"v":0.7755189398436004,"d":"0.78"},{"v":0.8413810578584624,"d":"0.84"},{"v":0.898248337765774,"d":"0.90"},{"v":0.9437637751977552,"d":"0.94"},{"v":0.9762205149779191,"d":"0.98"},{"v":0.9946021626078738,"d":"0.99"},{"v":0.9985005785353638,"d":"1.00"},{"v":0.9879399621328427,"d":"0.99"},{"v":0.9631377899929283,"d":"0.96"},{"v":0.9242166726484218,"d":"0.92"},{"v":0.8708658606130062,"d":"0.87"},{"v":0.8020380837196284,"d":"0.80"},{"v":0.7166359773813751,"d":"0.72"},{"v":0.6226651396824392,"d":"0.62"},{"v":0.5976968569693788,"d":"0.60"},{"v":0.8216876460716646,"d":"0.82"},{"v":0.9748094610472173,"d":"0.97"},{"v":0.945923006995577,"d":"0.95"},{"v":0.904423974453368,"d":"0.90"},{"$f":"1-POWER(IMABS(AW36),2)","v":{"v":0.9136440728832085,"d":"0.91"}},{"v":0.9790843335679164,"d":"0.98"},{"v":0.8912856546615698,"d":"0.89"},{"v":0.8753808084364965,"d":"0.88"},{"v":0.988478061301905,"d":"0.99"},{"v":0.8229463704709263,"d":"0.82"},{"v":0.870129967116145,"d":"0.87"},{"v":0.7994514937490221,"d":"0.80"},{"v":0.8082223145254098,"d":"0.81"},{"v":0.6700031347286345,"d":"0.67"},{"v":0.7526782843546396,"d":"0.75"},{"v":0.6685118565127333,"d":"0.67"},{"v":0.5416850251651106,"d":"0.54"},{"v":0.4704201668716036,"d":"0.47"},{"v":0.4329497998705675,"d":"0.43"},{"v":0.4058679274472863,"d":"0.41"},{"v":0.3161118398326367,"d":"0.32"}]
[]
[{"$nulls":15},"Absorbent against backing"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":14},"Eq 6.22","At top of porous absorber (z1)",{"$f":"IMPRODUCT(\"-j\",Q22,Q28)","v":"-633.676488433925-10655.4081479691j"},"-472.264819840332-9409.51380182372j","-336.595873344372-8310.49331944297j","-222.960993670692-7340.99127236867j","-128.162271866524-6485.68242871932j","-49.4434693584458-5731.03530503807j","15.5700349385997-5065.10304516491j","68.9234348180075-4477.33848623754j","112.377838696055-3958.43063068995j","147.449650139532-3500.16006052859j","175.444762768-3095.27111079033j","197.488248850215-2737.35886696533j","214.550137798582-2420.76926988455j","227.467809962067-2140.51080431047j","236.965471977888-1892.17641707931j","243.671132234668-1671.87445970698j","248.131459024869-1476.16758127388j","250.824880710212-1302.01861241655j","252.173278700756-1146.74258267803j","252.552633809395-1007.96410384928j","252.303020638625-883.579434518219j","251.738413251219-771.722620666504j","251.156885590581-670.73519213252j","250.851990976708-579.139000898104j","251.126436124497-495.611946454164j","252.309711858974-418.966613414881j","254.782252001603-348.132393686749j","259.010213804753-282.142807418214j","265.597514943354-220.132226270482j","275.365901472553-161.351818091863j","289.479993680806-105.227587934283j","309.640810166795-51.5145125952752j",{"$f":"IMPRODUCT(\"-j\",AW22,AW28)","v":"338.365312190807-0.675731250266182j"},"379.287749888789+45.2096048579027j","436.995657646916+80.368627674044j","514.250629882645+91.3300792251358j","600.358248719529+53.9758497272317j","649.20063104042-47.2696911052513j","602.800496565219-161.620476054794j","491.603185678813-200.389584284132j","399.239923402778-157.678403842669j","361.383599678789-78.729790970965j","382.766067910261-0.432292952746138j","460.532162412386+32.2613157394703j","521.688932895954-39.4350664163648j","451.35741976317-105.618383116883j","387.069919601839-49.6289400658947j","430.85040642644+12.9874608267274j","476.148518264094-47.0686119876451j"]
[{"$nulls":14},"Eq 6.23","At top of air layer (z2)",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",Q41,airImpedance,Q26),airImpedance^2),IMSUB(Q41,IMPRODUCT(\"j\",airImpedance,Q26)))","v":"-40.8594227289691-2680.52081844741j"},"-30.9260668430761-2377.35593281595j","-22.3881792731614-2107.40514553804j","-15.0662637899673-1866.88872705103j","-8.80142803674912-1652.43576867808j","-3.45255128999801-1461.03725984458j","1.1063114262808-1290.00400339269j","4.98834882701387-1136.9287180811j","8.29630597931136-999.651698536749j","11.1247781194433-876.229396539035j","13.5626072217943-764.905242219407j","15.6955620028862-664.081919827442j","17.6095868729366-572.294115339112j","19.3950945875312-488.180399500324j","21.1531289235343-410.452282991378j","23.0049017095966-337.85735528465j","25.1075767087272-269.131345529155j","27.6820856622738-202.929983388591j","31.065366169129-137.723636793548j","35.8155425961654-71.6211474323741j","42.9416450406934-2.05274588294431j","54.4576360608911+74.8424369026019j","74.8964887295719+165.47379565849j","116.169339950939+281.393113076016j","216.616366094022+442.558813234314j","526.342077023327+638.452873662099j","1206.50517339338+253.507962805479j","739.581804231806-434.836687790321j","358.788806226329-303.331794133349j","253.530073720439-126.290646071757j","260.828601236794+23.0050411445781j","373.158146764957+120.687244090393j",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",AW41,airImpedance,AW26),airImpedance^2),IMSUB(AW41,IMPRODUCT(\"j\",airImpedance,AW26)))","v":"502.452699662771+21.4444320499471j"},"390.988134340233-52.9722329851928j","367.187764910286+61.2370993483668j","551.796233333432+26.7293435160379j","349.347058355581-133.816176945574j","292.728868340173+107.165244969097j","671.613720743293-49.0223078423314j","261.505429006376-38.9098670762266j","578.682019999057+95.0607845545794j","324.66910714852-10.964756538284j","430.499329890263-27.7625442058011j","446.868847189607-45.205164136474j","509.13694062925+61.6040169089178j","410.032269465548+106.89211577625j","397.178487144617+54.5633606458242j","419.237706396291-20.6093135726434j","354.242299524829-32.5972505717304j"]
[{"$nulls":14},"Eq 6.24","Overall impedence (z3)",{"$f":"IMSUM((airDensity/porosity)*SQRT(8*airViscosity*Q15)*((panel_thickness/2*hole_radius)+1),IMPRODUCT(end_corrected_panel_thickness/porosity,\"j\",Q15,airDensity),Q42)","v":"-40.3438069621499-2675.53060706934j"},"-30.3797909672614-2371.75460993103j","-21.8094201433969-2101.11787317939j","-14.4530898514583-1859.83150244106j","-8.15179287847588-1644.51430188699j","-2.76428681500926-1452.14571400464j","1.83550223668996-1280.02358063656j","5.76089957938832-1125.72607231126j","9.1147949899716-987.077153819447j","11.9919370193765-862.114947319094j","14.4813300732187-749.062308637234j","16.6689149579149-646.298828147567j","18.6408184065751-552.333269826846j","20.4876463391607-465.775107960638j","22.3106471830633-385.303193556774j","24.2312495866146-309.628456844769j","26.4068470252737-237.445478364809j","29.0586146122513-167.36380002884j","32.5237477899473-97.8019457690153j","37.3606441009143-26.8105643530032j","44.5786230620139+48.2454329862637j","56.1919538607574+131.300233782364j","76.7339344324207+228.845529987183j","118.116045860996+352.525479795518j","218.678829161299+522.402195283379j","528.527180526586+728.074039820841j","1208.82020991244+354.104320543895j","742.034499985842-321.921094030796j","361.387346859422-176.588325475964j","256.283131620394+15.974087367246j","263.745364478431+182.691805242709j","376.248349774455+299.929576407876j",{"$f":"IMSUM((airDensity/porosity)*SQRT(8*airViscosity*AW15)*((panel_thickness/2*hole_radius)+1),IMPRODUCT(end_corrected_panel_thickness/porosity,\"j\",AW15,airDensity),AW42)","v":"505.726655705412+222.637147526779j"},"394.456769939966+172.858954533857j","370.862656315984+314.724036663138j","555.689645153547+311.258810394045j","353.471984490135+185.557351250688j","297.099075346691+465.649909604064j","676.243793781409+353.363123111333j","266.410820514448+412.752507961872j","583.879101265243+602.03465918412j","330.17522294843+558.09417721773j","436.332856373536+610.984512186722j","453.049253208603+671.76416513346j","515.684852714532+866.374878816246j","416.969540665013+1010.21686585245j","404.528269956012+1068.5111099049j","427.024530036521+1117.50855393939j","362.492151793937+1244.89686221332j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q43,airImpedance),IMSUM(Q43,airImpedance))","v":"0.957718559621839-0.303180404302121j"},"0.945114761374724-0.3397985324768j","0.929098753194383-0.380357276085192j","0.908803288502968-0.425068407514067j","0.883160871407338-0.474053375885418j","0.850868645170811-0.527285517709466j","0.81035453035115-0.584507668257418j","0.759751169566763-0.645116575752186j","0.696889623141032-0.708003715990568j","0.619333550169533-0.771341289896249j","0.524488397748195-0.832304442455746j","0.409840449693028-0.886730436805029j","0.273407349893965-0.928741001388109j","0.114508829391478-0.95040941499816j","-0.0650277316076271-0.941657912913063j","-0.25918039729169-0.89073521286331j","-0.455756558174406-0.785812898360663j","-0.634835750163176-0.618289552231808j","-0.769081540000834-0.387939682231245j","-0.827795427182042-0.108697052993806j","-0.785546529689298+0.18806738727627j","-0.633081272118869+0.456547182619766j","-0.385075662911954+0.646601910751878j","-0.0804546939691847+0.716508773600284j","0.222692548516149+0.642357522742399j","0.45043637973002+0.424759202871622j","0.51344289789496+0.106202769733946j","0.335890353082581-0.185019144326385j","-0.0145271234004605-0.231207826781252j","-0.233994561671081+0.0294315388570809j","-0.138255095241522+0.307064992687625j","0.0848650558889005+0.347560861972043j",{"$f":"IMDIV(IMSUB(AW43,airImpedance),IMSUM(AW43,airImpedance))","v":"0.150215939623904+0.205824289256668j"},"0.0212661503095877+0.209403137439958j","0.0918900395504398+0.364390215619434j","0.226523137300987+0.24841199780721j","-0.0186071675718579+0.246445561832467j","0.185853532164902+0.533524387687226j","0.313340699505654+0.222663542000384j","0.111253954477234+0.539551690791626j","0.392291789004929+0.366832950014192j","0.288641798246389+0.533861522840477j","0.358502365533811+0.461217556474955j","0.403918467526999+0.462107549259273j","0.523921291634581+0.4439104545569j","0.598444055658933+0.488485168367033j","0.626449020362052+0.487949912738494j","0.644525808833795+0.472631629355852j","0.70180624530118+0.47839872669922j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q45),2)","v":{"v":-0.009143196996927783,"d":"-0.01"}},{"v":-0.00870495484178857,"d":"-0.01"},{"v":-0.007896150658303513,"d":"-0.01"},{"v":-0.006606568260353773,"d":"-0.01"},{"v":-0.004699727973330292,"d":"-0.00"},{"v":-2.0074685209507948E-3,"d":"-0.00"},{"v":1.6763208876430236E-3,"d":"0.00"},{"v":0.006602764031709896,"d":"0.01"},{"v":0.013075591301897727,"d":"0.01"},{"v":0.021458568135593326,"d":"0.02"},{"v":0.0321812356959611,"d":"0.03"},{"v":0.04573993823897893,"d":"0.05"},{"v":0.06268857336457145,"d":"0.06"},{"v":0.08360967187424895,"d":"0.08"},{"v":0.10905176917018078,"d":"0.11"},{"v":0.1394163022250754,"d":"0.14"},{"v":0.17478404845103368,"d":"0.17"},{"v":0.214701599915748,"d":"0.21"},{"v":0.25801638778026637,"d":"0.26"},{"v":0.30293968140696215,"d":"0.30"},{"v":0.3475473075361786,"d":"0.35"},{"v":0.3907727729343087,"d":"0.39"},{"v":0.43362270284493964,"d":"0.43"},{"v":0.48014221957214187,"d":"0.48"},{"v":0.537784841811631,"d":"0.54"},{"v":0.6166866873915775,"d":"0.62"},{"v":0.725097362302064,"d":"0.73"},{"v":0.8529455869387914,"d":"0.85"},{"v":0.9463319035207983,"d":"0.95"},{"v":0.9443803296288629,"d":"0.94"},{"v":0.8865966189055066,"d":"0.89"},{"v":0.8719993695142243,"d":"0.87"},{"$f":"1-POWER(IMABS(AW45),2)","v":{"v":0.9350715334348951,"d":"0.94"}},{"v":0.955698076881312,"d":"0.96"},{"v":0.858775991392241,"d":"0.86"},{"v":0.886978747612749,"d":"0.89"},{"v":0.9389183583680325,"d":"0.94"},{"v":0.6808101923248003,"d":"0.68"},{"v":0.8522385530971507,"d":"0.85"},{"v":0.6965065305770751,"d":"0.70"},{"v":0.7115407390631976,"d":"0.71"},{"v":0.6316777867355376,"d":"0.63"},{"v":0.6587544195059336,"d":"0.66"},{"v":0.6233064845082293,"d":"0.62"},{"v":0.5284499885070388,"d":"0.53"},{"v":0.40324695253191933,"d":"0.40"},{"v":0.3694665075459216,"d":"0.37"},{"v":0.36120582467957507,"d":"0.36"},{"v":0.27860265234882475,"d":"0.28"}]
[]
[{"$nulls":15},"No air gap"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":15},"cot(ka * d)",{"$f":"IMDIV(IMCOS(IMPRODUCT(Q23,cavity_depth)),IMSIN(IMPRODUCT(Q23,cavity_depth)))","v":"0.471390449507333+0.886186615011617j"},"0.427649162645119+0.868635811616508j","0.384819474622242+0.853004109898209j","0.342829482705391+0.83940055092386j","0.301621456883961+0.827955530326306j","0.261157441595028+0.818824102706428j","0.221427046113224+0.812189377144343j","0.182458221501871+0.808265593290744j","0.144332062752145+0.807300084092428j","0.107202917009766+0.809572674798664j","0.0713252161108002+0.815389976486366j","0.037088227117015+0.825070286643331j","0.00505877303717024+0.838912179390754j","-0.0239711729040298+0.85713630675748j","-0.0489421731572921+0.879786129997542j","-0.0685141042022177+0.906571959978243j","-0.0811281841716658+0.936650816202651j","-0.085217685086256+0.968365858441055j","-0.0796515230021354+0.999040634037486j","-0.0644363373780152+1.02503334511736j","-0.0415072456923675+1.04233160592084j","-0.0151294682506902+1.04782992543675j","0.0087119034998344+1.04094103553368j","0.0241297216604458+1.02461764112449j","0.0276547422770641+1.00490254236175j","0.0198657927959113+0.988995241809638j","0.00560825458471943+0.982610928078564j","-0.0073390441422476+0.987341684687041j","-0.0115610665399089+0.998725748302585j","-0.0054142380016051+1.00735013375407j","0.00355970719083418+1.00608095215896j","0.00518743625066461+0.998669512823569j",{"$f":"IMDIV(IMCOS(IMPRODUCT(AW23,cavity_depth)),IMSIN(IMPRODUCT(AW23,cavity_depth)))","v":"-0.000466245910251478+0.995999811623606j"},"-0.00296584533847718+1.00044021476676j","0.000787210211711894+1.00205177703593j","0.00111381337012677+0.998875032509218j","-0.00111611184189195+0.999858575917537j","0.000558543166194902+1.00055360730524j","-0.000222390493335386+0.999508041300363j","0.000137136717034864+1.0003375858471j","-0.000157617575640357+0.999817468249532j","0.000155386423794424+1.00001906833449j","-0.0000474954504600398+1.00008747371087j","-0.0000580039703964221+0.999978323842515j","-0.0000132559944218029+0.999964752492989j","-3.42853504271342E-06+0.999977901614743j","-8.08879915400567E-06+0.999989883687751j","-6.61559945582199E-06+1.00000310597872j","3.60653631385984E-06+1.00000175809976j"]
[{"$nulls":14},"Eq 6.25","At top of porous absorber (z1)",{"$f":"IMPRODUCT(\"-j\",Q22,Q50)","v":"707.664121647636-2491.2092778136j"},"722.548452738621-2200.30564997462j","733.285861663666-1943.25200032942j","740.707869679727-1716.10603751989j","745.533596333022-1515.40519077236j","748.384801749866-1338.11536390168j","749.798108474614-1181.58683448169j","750.234222431472-1043.5167302974j","750.083701497272-921.917552538507j","749.668445612006-815.091144358287j","749.237578774694-721.607224615058j","748.955767188154-640.284939741637j","748.881379763318-570.174529847079j","748.931624102935-510.533711035029j","748.832844932155-460.789243261584j","748.058598213167-420.468295266008j","745.76944184746-389.078344547762j","740.790660978402-365.914874124961j","731.696416788122-349.797719663616j","717.09134693037-338.799832025909j","696.140263791598-330.136778707747j","669.231549710855-320.457595967409j","638.414638345879-306.658991624423j","607.180190417869-286.972316998654j","579.492147265517-261.739080442129j","558.490794492145-233.425436896788j","545.394768287645-205.908499510639j","538.817774853101-183.247867847568j","534.736181504078-167.876826858376j","528.11080951315-158.478096932544j","516.8300990339-149.875312629198j","504.447596515035-137.66204740301j",{"$f":"IMPRODUCT(\"-j\",AW22,AW50)","v":"496.183620930384-123.524309934723j"},"491.611939640909-112.772091144351j","485.496715518666-105.516586886154j","478.007008631171-96.8368661776315j","473.247494285423-88.0537189222683j","468.445536235458-81.7171416812004j","463.452320458513-74.6692807764297j","459.622529833356-68.829353912665j","455.565962326666-63.085606291754j","452.121243070911-58.1181255108602j","448.939340019646-53.3232655360495j","445.935568239773-48.9878110741924j","443.218734610983-45.0328129630394j","440.741484323248-41.3856641740997j","438.471380084474-38.0281175606993j","436.391348214625-34.9453614209614j","434.478655175065-32.1159193850759j"]
[{"$nulls":14},"Eq 6.26","Overall impedence (z2)",{"$f":"IMSUM(IMPRODUCT(\"j\",Q15*airDensity*end_corrected_panel_thickness/porosity),Q51)","v":"707.664121647636-2486.21906643553j"},"722.548452738621-2194.7043270897j","733.285861663666-1936.96472797077j","740.707869679727-1709.04881290992j","745.533596333022-1507.48372398127j","748.384801749866-1329.22381806174j","749.798108474614-1171.60641172556j","750.234222431472-1032.31408452756j","750.083701497272-909.343007821205j","749.668445612006-800.976695138346j","749.237578774694-705.764291032885j","748.955767188154-622.501848061762j","748.881379763318-550.213684334813j","748.931624102935-488.128419495344j","748.832844932155-435.64015382698j","748.058598213167-392.239396826127j","745.76944184746-357.392477383416j","740.790660978402-330.34869076521j","731.696416788122-309.876028639083j","717.09134693037-293.989248946538j","696.140263791598-279.838599838539j","669.231549710855-263.999799087647j","638.414638345879-243.28725729573j","607.180190417869-215.839950279152j","579.492147265517-181.895698393064j","558.490794492145-143.804270738046j","545.394768287645-105.312141772223j","538.817774853101-70.332274088043j","534.736181504078-41.133358200991j","528.11080951315-16.213363493541j","516.8300990339+9.811451468933j","504.447596515035+41.580284914473j",{"$f":"IMSUM(IMPRODUCT(\"j\",AW15*airDensity*end_corrected_panel_thickness/porosity),AW51)","v":"496.183620930384+77.668405542109j"},"491.611939640909+113.059096374699j","485.496715518666+147.970350428617j","478.007008631171+187.692600700375j","473.247494285423+231.319809273994j","468.445536235458+276.767522953767j","463.452320458513+327.716150177234j","459.622529833356+382.833021125434j","455.565962326666+443.888268337787j","452.121243070911+510.940808245154j","448.939340019646+585.423790856473j","445.935568239773+667.981518195742j","443.218734610983+759.738048944289j","440.741484323248+861.939085902099j","438.471380084474+975.919631698381j","436.391348214625+1103.17250609107j","434.478655175065+1245.37819339997j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q52,airImpedance),IMSUM(Q52,airImpedance))","v":"0.875357737313659-0.276405196636063j"},"0.846178970643273-0.297170309827587j","0.8128425014977-0.316123698176938j","0.775582421410337-0.332305615714091j","0.734931822601356-0.344766077912599j","0.691732595277906-0.352673602458149j","0.647098300902603-0.355430554167163j","0.602327785423222-0.352771573531328j","0.55878068814178-0.344821950651865j","0.517737532616717-0.332101643282676j","0.480271234539103-0.315475053814409j","0.44715156871313-0.296060582475459j","0.418792081263598-0.275121522113561j","0.395235755509657-0.253958692681757j","0.376166686703526-0.233817092304177j","0.36093264294662-0.215807746692438j","0.348567586789135-0.2008356055466j","0.3378129028692-0.18951714009572j","0.327150735705735-0.18206909648686j","0.314882691969779-0.178156355544952j","0.299310039025562-0.176710394611647j","0.279084532856404-0.17578353958312j","0.253765017123487-0.172594061801657j","0.22447029797461-0.164003196000989j","0.194234713335202-0.147603693426339j","0.167426446076602-0.123181237018805j","0.147860440457833-0.0935902718742418j","0.136336174885196-0.0637866905872851j","0.129525289425592-0.0377612558136959j","0.12201098063616-0.0151183182371783j","0.111199993531481+0.00937374437274607j","0.100954907614047+0.0407252809297425j",{"$f":"IMDIV(IMSUB(AW52,airImpedance),IMSUM(AW52,airImpedance))","v":"0.0975050726639089+0.0770569729917136j"},"0.100371648905783+0.112377554478878j","0.104383828834066+0.147418450171918j","0.111763579309651+0.187009813083697j","0.126833759105685+0.227784040918521j","0.146401006952858+0.2678803324295j","0.172555174989048+0.309224972063383j","0.205593132135037+0.348330014498386j","0.245328562232854+0.385471803424256j","0.291508371506768+0.418206942941101j","0.343595632216776+0.445581501937779j","0.400156837034071+0.466232739139045j","0.459671527549449+0.479178629057149j","0.52031914529919+0.484018895982665j","0.58020553819386+0.480883422162967j","0.637598255318064+0.470418494712049j","0.691095797364956+0.453684844516096j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q54),2)","v":{"v":0.1573489989976905,"d":"0.16"}},{"v":0.19567095659806688,"d":"0.20"},{"v":0.239352875209898,"d":"0.24"},{"v":0.2880448853641573,"d":"0.29"},{"v":0.34101156764861273,"d":"0.34"},{"v":0.3971273467592843,"d":"0.40"},{"v":0.45493291013338755,"d":"0.45"},{"v":0.5127534558153878,"d":"0.51"},{"v":0.5688619649084415,"d":"0.57"},{"v":0.6216563458489002,"d":"0.62"},{"v":0.6698150316950817,"d":"0.67"},{"v":0.712403606101679,"d":"0.71"},{"v":0.7489213407408213,"d":"0.75"},{"v":0.7792936799780835,"d":"0.78"},{"v":0.8038281911609113,"d":"0.80"},{"v":0.8231546437231003,"d":"0.82"},{"v":0.8381656969847293,"d":"0.84"},{"v":0.8499656962650236,"d":"0.85"},{"v":0.8598232402316548,"d":"0.86"},{"v":0.869109203276806,"d":"0.87"},{"v":0.8791869369747125,"d":"0.88"},{"v":0.8912119707319525,"d":"0.89"},{"v":0.9058146059151222,"d":"0.91"},{"v":0.922716037028651,"d":"0.92"},{"v":0.9404860258224952,"d":"0.94"},{"v":0.9567947680006756,"d":"0.96"},{"v":0.9693781511581211,"d":"0.97"},{"v":0.9773437055215952,"d":"0.98"},{"v":0.9817972869585893,"d":"0.98"},{"v":0.984884757057882,"d":"0.98"},{"v":0.987546694355033,"d":"0.99"},{"v":0.9881495581218328,"d":"0.99"},{"$f":"1-POWER(IMABS(AW54),2)","v":{"v":0.9845549837181602,"d":"0.98"}},{"v":0.9772968173452811,"d":"0.98"},{"v":0.9673718168268501,"d":"0.97"},{"v":0.952536232150296,"d":"0.95"},{"v":0.9320276282539506,"d":"0.93"},{"v":0.9068068726606497,"d":"0.91"},{"v":0.874604628236899,"d":"0.87"},{"v":0.8363976650184595,"d":"0.84"},{"v":0.7912253853176123,"d":"0.79"},{"v":0.7401258222173308,"d":"0.74"},{"v":0.6833991666524271,"d":"0.68"},{"v":0.6225015387297912,"d":"0.62"},{"v":0.5590899282152673,"d":"0.56"},{"v":0.49499369536684246,"d":"0.49"},{"v":0.43211266773800705,"d":"0.43"},{"v":0.3721749046482108,"d":"0.37"},{"v":0.3165566607209016,"d":"0.32"}]

{"sheet":"Slotted Panel","index":2,"n_rows":57,"n_cols":65,"rows_kept":57}
[]
[null,"Slotted Panel with Porous Absorber",{"$nulls":13},"Cox & D'Antonio Appendix B.5"]
[null,"Properties of panel",{"$nulls":4},"Display options",{"$nulls":8},"Slotted Absorber"]
[null,"Panel thickness (tp)",{"v":5,"d":"5.0"},"mm",{"$f":"slotted_panel_thickness_mm/25.4","v":{"v":0.1968503937007874,"d":"0.197"}},"in","Start graph at",62.5,"Hz",{"$nulls":6},"Panel thickness (tp)",{"$f":"slotted_panel_thickness_mm/1000","v":0.005},"m"]
[null,"Distance between slots (D)",40.5,"mm",{"$f":"C5/25.4","v":{"v":1.594488188976378,"d":"1.594"}},"in",{"$nulls":4},"To see the graph in the standard",{"$nulls":4},"Slot width (w)",{"$f":"slot_width_mm/1000","v":0.01},"m"]
[null,"Slot width (w)",{"v":10,"d":"10.0"},"mm",{"$f":"slot_width_mm/25.4","v":{"v":0.3937007874015748,"d":"0.394"}},"in",{"$nulls":4},"analysis frequencies, select",{"$nulls":4},"Distance between slots (D)",{"$f":"slotted_repeat_distance_mm/1000","v":0.0405},"m"]
[null,"Open Area (e)",{"$f":"slot_width/(slot_width+slotted_repeat_distance)","v":{"v":0.198019801980198,"d":"19.80%"}},{"$nulls":3},"Show subdivisions of",{"$nulls":3},"\"Whole Octaves\" and set the",{"$nulls":4},"Cavity depth (d)",{"$f":"slotted_cavity_depth_mm/1000","v":0.05},"m"]
[null,"Properties of cavity",{"$nulls":8},"starting frequency to 62.5Hz",{"$nulls":4},"Absorber thickness (ta)",{"$f":"slotted_absorber_thickness_mm/1000","v":0.025},"m"]
[null,"Cavity depth (d)",{"v":50,"d":"50.0"},"mm",{"$f":"slotted_cavity_depth_mm/25.4","v":{"v":1.968503937007874,"d":"1.969"}},"in",{"$nulls":9},"Cavity air gap (d - ta)",{"$f":"slotted_airGap_mm/1000","v":0.025},"m"]
[null,"Absorber thickness (ta)",{"v":25,"d":"25.0"},"mm",{"$f":"slotted_absorber_thickness_mm/25.4","v":{"v":0.984251968503937,"d":"0.984"}},"in",{"$nulls":8},"Eq 6.10","Slot end correction (d)",{"$f":"-LN(SIN(PI()*slotted_porosity/2))/PI()","v":{"v":0.37687352199615437,"d":"0.37687"}},{"$nulls":3},"End corrected panel thickness (t')",{"$f":"slotted_panel_thickness+2*slot_width*slotted_delta","v":{"v":0.012537470439923088,"d":"0.0125"}},"m"]
[null,"Air space in cavity (d - ta)",{"$f":"slotted_cavity_depth_mm-slotted_absorber_thickness_mm","v":{"v":25,"d":"25.0"}},"mm",{"$f":"C11/25.4","v":{"v":0.984251968503937,"d":"0.984"}},"in","This is ignored for the \"No Air Gap\" plot.  Cavity assumed to be filled with absorber.",{"$nulls":8},"Octave subdivisions",6]
[null,"Absorber flow resisitivity",{"v":16500,"d":"16,500"},"rayls/m"]
[{"$nulls":15},"Resistance terms"]
[null,"This plot is a simplification of reality because it is only calculated for normal incident sound.",{"$nulls":12},"Eq 6.20","Porous layer next to panel",{"$f":"slotted_sigma*slotted_absorber_thickness*slotted_porosity","v":{"v":81.68316831683167,"d":"81.68"}},"Pa s"]
[{"$nulls":14},"Eq 6.21","Porous layer against backing",{"$f":"slotted_sigma*slotted_absorber_thickness","v":{"v":412.5,"d":"412.50"}},"Pa s"]
[{"$nulls":14},"Eq 6.11","Mass term for air in slots",{"$f":"end_corrected_slotted_panel_thickness*airDensity/slotted_porosity","v":{"v":0.07623781887846934,"d":"0.0762"}},"Kg m-2"]
[]
[{"$nulls":15},"Interval number",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]
[{"$nulls":15},"Angular values",{"$f":"start_freq_slot","v":62.5},{"$f":"ROUND(POWER(2,LOG(start_freq_slot,2)+R18/subdiv_slot),0)","v":70},79,88,99,111,125,140,157,177,198,223,250,281,315,354,397,445,500,561,630,707,794,891,{"v":1000,"d":"1,000"},{"v":1122,"d":"1,122"},{"v":1260,"d":"1,260"},{"v":1414,"d":"1,414"},{"v":1587,"d":"1,587"},{"v":1782,"d":"1,782"},{"v":2000,"d":"2,000"},{"v":2245,"d":"2,245"},{"v":2520,"d":"2,520"},{"v":2828,"d":"2,828"},{"v":3175,"d":"3,175"},{"v":3564,"d":"3,564"},{"v":4000,"d":"4,000"},{"v":4490,"d":"4,490"},{"v":5040,"d":"5,040"},{"v":5657,"d":"5,657"},{"v":6350,"d":"6,350"},{"v":7127,"d":"7,127"},{"v":8000,"d":"8,000"},{"v":8980,"d":"8,980"},{"v":10079,"d":"10,079"},{"v":11314,"d":"11,314"},{"v":12699,"d":"12,699"},{"v":14254,"d":"14,254"},{"v":16000,"d":"16,000"}]
[{"$nulls":14},"2pf","Angular frequency (w)",{"$f":"2*PI()*Q19","v":{"v":392.6990816987241,"d":"392.7"}},{"v":439.822971502571,"d":"439.8"},{"v":496.37163926718733,"d":"496.4"},{"v":552.9203070318035,"d":"552.9"},{"v":622.0353454107791,"d":"622.0"},{"v":697.4335690969341,"d":"697.4"},{"v":785.3981633974482,"d":"785.4"},{"v":879.645943005142,"d":"879.6"},{"v":986.460093227195,"d":"986.5"},{"v":1112.1237993707869,"d":"1112.1"},{"v":1244.0706908215582,"d":"1244.1"},{"v":1401.1503235010478,"d":"1401.2"},{"v":1570.7963267948965,"d":"1570.8"},{"v":1765.5750713174637,"d":"1765.6"},{"v":1979.2033717615698,"d":"1979.2"},{"v":2224.2475987415737,"d":"2224.2"},{"v":2494.4245669502957,"d":"2494.4"},{"v":2796.0174616949157,"d":"2796.0"},{"v":3141.592653589793,"d":"3141.6"},{"v":3524.866957327748,"d":"3524.9"},{"v":3958.4067435231395,"d":"3958.4"},{"v":4442.212012175967,"d":"4442.2"},{"v":4988.849133900591,"d":"4988.8"},{"v":5598.318108697012,"d":"5598.3"},{"v":6283.185307179586,"d":"6283.2"},{"v":7049.733914655496,"d":"7049.7"},{"v":7916.813487046279,"d":"7916.8"},{"v":8884.424024351934,"d":"8884.4"},{"v":9971.415082494002,"d":"9971.4"},{"v":11196.636217394023,"d":"11196.6"},{"v":12566.370614359172,"d":"12566.4"},{"v":14105.75101461817,"d":"14105.8"},{"$f":"2*PI()*AW19","v":{"v":15833.626974092558,"d":"15833.6"}},{"v":17768.84804870387,"d":"17768.8"},{"v":19949.113350295185,"d":"19949.1"},{"v":22393.272434788047,"d":"22393.3"},{"v":25132.741228718343,"d":"25132.7"},{"v":28211.50202923634,"d":"28211.5"},{"v":31667.253948185116,"d":"31667.3"},{"v":35543.97928271492,"d":"35544.0"},{"v":39898.22670059037,"d":"39898.2"},{"v":44780.26168426891,"d":"44780.3"},{"v":50265.48245743669,"d":"50265.5"},{"v":56423.00405847268,"d":"56423.0"},{"v":63328.22471106305,"d":"63328.2"},{"v":71087.95856542984,"d":"71088.0"},{"v":79790.17021587357,"d":"79790.2"},{"v":89560.52336853782,"d":"89560.5"},{"v":100530.96491487337,"d":"100531.0"}]
[{"$nulls":14},"2p/l","Wave number (k)",{"$f":"Q20/sound_velocity","v":{"v":1.143621965612716,"d":"1.1436"}},{"v":1.280856601486242,"d":"1.2809"},{"v":1.4455381645344731,"d":"1.4455"},{"v":1.6102197275827042,"d":"1.6102"},{"v":1.8114971935305424,"d":"1.8115"},{"v":2.031072610928184,"d":"2.0311"},{"v":2.287243931225432,"d":"2.2872"},{"v":2.561713202972484,"d":"2.5617"},{"v":2.872778377619143,"d":"2.8728"},{"v":3.238737406615212,"d":"3.2387"},{"v":3.622994387061085,"d":"3.6230"},{"v":4.080443173306171,"d":"4.0804"},{"v":4.574487862450864,"d":"4.5745"},{"v":5.1417243573947715,"d":"5.1417"},{"v":5.76385470668809,"d":"5.7639"},{"v":6.477474813230424,"d":"6.4775"},{"v":7.2642867255719725,"d":"7.2643"},{"v":8.142588395162539,"d":"8.1426"},{"v":9.148975724901728,"d":"9.1490"},{"v":10.26515076333974,"d":"10.2652"},{"v":11.52770941337618,"d":"11.5277"},{"v":12.936651675011044,"d":"12.9367"},{"v":14.528573451143945,"d":"14.5286"},{"v":16.30347474177488,"d":"16.3035"},{"v":18.297951449803456,"d":"18.2980"},{"v":20.53030152667948,"d":"20.5303"},{"v":23.05541882675236,"d":"23.0554"},{"v":25.873303350022088,"d":"25.8733"},{"v":29.038848950838087,"d":"29.0388"},{"v":32.60694948354976,"d":"32.6069"},{"v":36.59590289960691,"d":"36.5959"},{"v":41.07890100480876,"d":"41.0789"},{"$f":"AW20/sound_velocity","v":{"v":46.11083765350472,"d":"46.1108"}},{"v":51.746606700044175,"d":"51.7466"},{"v":58.09599585312598,"d":"58.0960"},{"v":65.21389896709952,"d":"65.2139"},{"v":73.19180579921382,"d":"73.1918"},{"v":82.15780200961753,"d":"82.1578"},{"v":92.22167530700943,"d":"92.2217"},{"v":103.51151135153816,"d":"103.5115"},{"v":116.19199170625195,"d":"116.1920"},{"v":130.40949998274925,"d":"130.4095"},{"v":146.38361159842765,"d":"146.3836"},{"v":164.31560401923505,"d":"164.3156"},{"v":184.42505266256904,"d":"184.4251"},{"v":207.02302270307632,"d":"207.0230"},{"v":232.36568546105414,"d":"232.3657"},{"v":260.8189999654985,"d":"260.8190"},{"v":292.7672231968553,"d":"292.7672"}]
[{"$nulls":15},"Properties of porous absorber"]
[{"$nulls":14},"Eq 5.11","Delany & Bazley's term",{"$f":"(airDensity*Q19)/slotted_sigma","v":{"v":0.004561054228691726,"d":"0.005"}},{"v":0.005108380736134733,"d":"0.005"},{"v":0.005765172545066342,"d":"0.006"},{"v":0.00642196435399795,"d":"0.006"},{"v":0.007224709898247693,"d":"0.007"},{"v":0.008100432310156506,"d":"0.008"},{"v":0.009122108457383453,"d":"0.009"},{"v":0.010216761472269466,"d":"0.010"},{"v":0.011457368222473617,"d":"0.011"},{"v":0.012916905575654967,"d":"0.013"},{"v":0.014449419796495387,"d":"0.014"},{"v":0.016273841487972077,"d":"0.016"},{"v":0.018244216914766905,"d":"0.018"},{"v":0.020506499812198,"d":"0.021"},{"v":0.0229877133126063,"d":"0.023"},{"v":0.025833811151309935,"d":"0.026"},{"v":0.028971816460649846,"d":"0.029"},{"v":0.03247470610828509,"d":"0.032"},{"v":0.03648843382953381,"d":"0.036"},{"v":0.04094002275673693,"d":"0.041"},{"v":0.0459754266252126,"d":"0.046"},{"v":0.0515946454349608,"d":"0.052"},{"v":0.05794363292129969,"d":"0.058"},{"v":0.06502238908422923,"d":"0.065"},{"v":0.07297686765906762,"d":"0.073"},{"v":0.08188004551347386,"d":"0.082"},{"v":0.0919508532504252,"d":"0.092"},{"v":0.1031892908699216,"d":"0.103"},{"v":0.11581428897494031,"d":"0.116"},{"v":0.13004477816845847,"d":"0.130"},{"v":0.14595373531813524,"d":"0.146"},{"v":0.16383306789460678,"d":"0.164"},{"$f":"(airDensity*AW19)/slotted_sigma","v":{"v":0.1839017065008504,"d":"0.184"}},{"v":0.2063785817398432,"d":"0.206"},{"v":0.23170155481753968,"d":"0.232"},{"v":0.26008955633691694,"d":"0.260"},{"v":0.2919074706362705,"d":"0.292"},{"v":0.32766613578921355,"d":"0.328"},{"v":0.3678034130017008,"d":"0.368"},{"v":0.4128301403473455,"d":"0.413"},{"v":0.46340310963507936,"d":"0.463"},{"v":0.5201061358061749,"d":"0.520"},{"v":0.583814941272541,"d":"0.584"},{"v":0.6553322715784271,"d":"0.655"},{"v":0.7355338491357425,"d":"0.736"},{"v":0.825660280694691,"d":"0.826"},{"v":0.9267332424024997,"d":"0.927"},{"v":1.0402122716123499,"d":"1.040"},{"v":1.167629882545082,"d":"1.168"}]
[{"$nulls":14},"Eq 5.9","Characteristic impedance (za)",{"$f":"IMPRODUCT(airImpedance,COMPLEX(1+0.0571*(Q23^-0.754),-0.087*(Q23^-0.732),\"j\"))","v":"1787.98109383187-1860.07330550798j"},"1675.40774059031-1711.99490363636j","1565.41330293132-1566.93579610344j","1475.41512120007-1447.94783802212j","1385.17215192957-1328.34006026248j","1304.86187918287-1221.62472025992j","1228.49730841642-1119.89189949642j","1161.74612248817-1030.73852997311j","1099.80194840973-947.797780237007j","1040.47478667801-868.156061440356j","989.648826069252-799.751960774618j","940.240145075734-733.086248705973j","896.747341761659-674.251849560947j","855.975666823481-618.958037179421j","819.461984316342-569.312746457753j","785.258024388967-522.689583161486j","754.471328356912-480.617501975188j","726.352262298463-442.094085471727j","700.033793944169-405.945928210378j","676.210510040036-373.141384293384j","654.206880950893-342.765379810652j","634.16046231476-315.020794078084j","615.670200336631-289.364750101195j","598.83977640899-265.952301789261j","583.391069650505-244.407333458401j","569.264880747758-224.65674465605j","556.217669359518-206.368303410995j","544.331000098595-189.664157007313j","533.424023966921-174.297806810521j","523.387343326197-160.121554104494j","514.226920655183-147.150003232176j","505.819666906199-135.214687261599j",{"$f":"IMPRODUCT(airImpedance,COMPLEX(1+0.0571*(AW23^-0.754),-0.087*(AW23^-0.732),\"j\"))","v":"498.114255953493-124.247894219243j"},"491.065969240375-114.190850666125j","484.581706952174-104.915057433802j","478.64727612184-96.4041744190449j","473.215537088693-88.5944097700933j","468.230395028122-81.4085297116035j","463.661415741753-74.8057669843383j","459.47595045278-68.7418395768945j","455.637192704429-63.1660712550408j","452.122417387422-58.0478963220357j","448.897539882491-53.3399202861517j","445.941563756864-49.0135268884152j","443.234580648276-45.0414810917081j","440.750552378769-41.3873093445759j","438.475817609284-38.0325059447824j","436.390221636718-34.9488209316043j","434.47800714076-32.1142959642295j"]
[{"$nulls":14},"Eq 5.10","Complex wave number (ka)",{"$f":"IMPRODUCT(Q21,COMPLEX(1+0.0978*(Q23^-0.7),-0.189*(Q23^-0.595),\"j\"))","v":"6.01078257968505-5.34072820862549j"},"6.31633902975749-5.59157013123828j","6.66709248260904-5.87229739959502j","7.0035432736245-6.13457601591376j","7.39880028800231-6.43430026466033j","7.81347841006123-6.73945653161776j","8.279421530093-7.07159899447689j","8.76111926303513-7.40373600247072j","9.28903268053413-7.75547548439094j","9.88999323816153-8.14138406847731j","10.5017713774848-8.51958562659091j","11.2090248787988-8.93989750443944j","11.9517238370672-9.36342580735007j","12.7822558260226-9.81736933446734j","13.67072908502-10.2821715251544j","14.6661312719665-10.7799163603406j","15.739464658836-11.2922172617241j","16.9129939484679-11.8264629228022j","18.2314185809778-12.3980082748223j","19.666723950154-12.9896972443607j","21.2622136312795-13.6145092912403j","23.0137964259691-14.2653993096599j","24.9627414157861-14.9518996500243j","27.1047487635994-15.6664118807088j","29.479750231586-16.4160652676826j","32.1049958322791-17.1995140706516j","35.0399993113066-18.0268207730063j","38.279723812632-18.8886570282827j","41.882389193265-19.7925944223315j","45.9048776525266-20.7437222369332j","50.3623120009455-21.7363299732656j","55.3309260345449-22.777795524402j",{"$f":"IMPRODUCT(AW21,COMPLEX(1+0.0978*(AW23^-0.7),-0.189*(AW23^-0.595),\"j\"))","v":"60.8655869633464-23.869113475223j"},"67.0207019421944-25.0102613034112j","73.9097430472394-26.2104984823139j","81.5855689413976-27.4665325742457j","90.1402434561477-28.780833470296j","99.7041030038291-30.1598264571145j","110.386902490126-31.6048284535121j","122.317125732133-33.1181807831849j","135.660998218333-34.7050303763672j","150.564541655206-36.3660647312322j","167.249585934686-38.1083824299556j","185.917634463127-39.9342917513151j","206.788405007319-41.8459214437167j","230.175449787262-43.8514159074851j","256.334277845578-45.9510804061218j","285.632766921278-48.1519030253458j","318.456250929939-50.4588865686111j"]
[{"$nulls":15},"Intermediate values"]
[{"$nulls":15},"For air in slots - cot(kair * tp)",{"$f":"COS(Q21*end_corrected_slotted_panel_thickness)/SIN(Q21*end_corrected_slotted_panel_thickness)","v":69.73933906987908},62.26618139212106,55.17126768555044,49.5274455351805,44.02280705661378,39.26184846148641,34.862499980328494,31.125060654891776,27.752371558342357,24.613623811608978,22.000045779143893,19.53006262874676,17.416907932070817,15.490987847359587,13.814022309295694,12.286497952693523,10.949492129229546,9.7614694423923,8.67974622973973,7.727119558344682,6.8708160487760725,6.111339103489498,5.429081846210957,4.823938886212508,4.2822677440714845,3.7988526142029517,3.3626364647289675,2.9738544222726326,2.624252519049906,2.308319705455334,2.0243733073344305,1.766861652592385,{"$f":"COS(AW21*end_corrected_slotted_panel_thickness)/SIN(AW21*end_corrected_slotted_panel_thickness)","v":1.5326253822022522},1.3187952419803086,1.1210779452602482,0.9375520757293888,0.7651966354781445,0.6004431915448315,0.4400751083191271,0.28001629463526007,0.11453965374785893,-0.06429730996883695,-0.2708284967784374,-0.5324966480860758,-0.9157102724473571,-1.6456022245762034,-4.303547975389529,7.744226441303989,1.7107725670589575]
[{"$nulls":15},"For air gap - cot(kair * tair)",{"$f":"COS(Q21*slotted_airGap)/SIN(Q21*slotted_airGap)","v":34.9670622651317},31.21842632917097,27.65930799554651,24.827910285041092,22.066084554616133,19.67709905675136,17.469231961642972,15.593196982516345,13.899854876925883,12.323490585319952,11.010383069293052,9.768829466819867,8.70599423024322,7.7365963419137636,6.891701449158478,6.1211723724683855,5.445721335784206,4.844399732251479,4.295565420730742,3.8107583768975593,3.3732997001785727,2.9834254364987953,2.631045466714902,2.3160735224086073,2.0313835984843225,1.7741717093729052,1.5384270283893553,1.3241201269001814,1.12652164833384,0.9421541498958234,0.7695541419463824,0.6046393440670944,{"$f":"COS(AW21*slotted_airGap)/SIN(AW21*slotted_airGap)","v":0.4442062237783937},0.28445081951349993,0.11895276589207908,-0.05962164357419679,-0.26494979390389606,-0.5246195685338296,-0.9035002075488505,-1.6172003033919775,-4.143872704822372,8.388930700719035,1.7546750895898897,0.6907617936716768,0.10211539750115264,-0.4994238555060357,-1.9490790609444009,4.134862998422441,0.5923845053596711]
[{"$nulls":15},"For absorbent layer - cot(ka * ta)",{"$f":"IMDIV(IMCOS(IMPRODUCT(Q25,slotted_absorber_thickness)),IMSIN(IMPRODUCT(Q25,slotted_absorber_thickness)))","v":"3.66881633109156+3.34890125930273j"},"3.49789300000511+3.18978570485578j","3.32314417543086+3.02493816948229j","3.17360259653909+2.8821750918285j","3.01678872153436+2.73087852762018j","2.87054077406814+2.58843085152275j","2.72465545345849+2.44521432727373j","2.59077166420985+2.31299308528383j","2.46030609637073+2.18365944579318j","2.32874732725525+2.05304952507051j","2.20998028033431+1.9352808273088j","2.08817381794047+1.81500235193828j","1.97481233437422+1.70390003407229j","1.86232790729036+1.59487075743785j","1.75551251581138+1.49287723004573j","1.64923023575381+1.39333244437252j","1.5474117840424+1.30023326267318j","1.44831355365456+1.21219719981512j","1.3492287972298+1.12717372292226j","1.253190129825+1.04807988587775j","1.15802333865384+0.973372835823309j","1.06479038684495+0.904160272387209j","0.972095594594624+0.839677002497723j","0.880913375247307+0.780873014526009j","0.790220953302627+0.727345394970333j","0.70006823359683+0.679445229051496j","0.60917876424747+0.636931655439741j","0.518372633546366+0.600690996096958j","0.426526419511992+0.570857595571136j","0.332743298549939+0.548039982739895j","0.237061876693731+0.53342069779453j","0.138116242686884+0.528447291366404j",{"$f":"IMDIV(IMCOS(IMPRODUCT(AW25,slotted_absorber_thickness)),IMSIN(IMPRODUCT(AW25,slotted_absorber_thickness)))","v":"0.0351056736878909+0.535640571033575j"},"-0.0725099627429699+0.559005400595155j","-0.185252812008051+0.605491229431279j","-0.299418911873208+0.686197791348857j","-0.402734943410387+0.818543801766512j","-0.458566745243582+1.02289955775976j","-0.382399349818481+1.2854090177286j","-0.0963634046440001+1.46004380247214j","0.234298766750293+1.34281131323495j","0.333380754375927+1.05550056117349j","0.22269179626522+0.837948031554773j","0.0271065984832101+0.762234516255998j","-0.167744274418449+0.844718216302587j","-0.21542739125363+1.09380334844241j","0.0610740236868856+1.21406604322359j","0.172323193606529+0.959251706389707j","-0.0294079659463745+0.854169768862003j"]
[{"$nulls":15},"No air gap - cot(ka * d)",{"$f":"IMDIV(IMCOS(IMPRODUCT(Q25,slotted_cavity_depth)),IMSIN(IMPRODUCT(Q25,slotted_cavity_depth)))","v":"1.760066446025+1.74230986697867j"},"1.67090333112785+1.66606169162275j","1.57928972212874+1.58736775154553j","1.500462087851+1.51949834693509j","1.41730065818931+1.44789974060637j","1.3392012811387+1.3808430883343j","1.26068287278369+1.31382730409382j","1.18799219160334+1.25237560111516j","1.11647602296562+1.19272444906784j","1.04356390789848+1.13303198584828j","0.976939548027061+1.07977438068545j","0.907688821400008+1.02605588995555j","0.842266805418555+0.977178606688961j","0.776276585883386+0.930078686362435j","0.712469530822161+0.88699744845148j","0.647709789433058+0.846122573615893j","0.584308366826597+0.809260412368602j","0.521143086452055+0.776015277394977j","0.456358907399041+0.745922025880322j","0.391823550435954+0.72038628835279j","0.325999404142822+0.699355073058631j","0.259551725459973+0.68376350538988j","0.19147825089965+0.674281865792092j","0.122614363698966+0.672183272156145j","0.0525728403638174+0.678955620971907j","-0.0177487019693623+0.696671079756049j","-0.0875282154469209+0.728447470557102j","-0.152521238602997+0.777432839345096j","-0.206708971890385+0.847514283828196j","-0.238360630853697+0.940628373214493j","-0.229336464322289+1.04945819203309j","-0.162422155881062+1.14989156659061j",{"$f":"IMDIV(IMCOS(IMPRODUCT(AW25,slotted_cavity_depth)),IMSIN(IMPRODUCT(AW25,slotted_cavity_depth)))","v":"-0.0433642177213125+1.19728958393032j"},"0.0778459860176141+1.15914812515779j","0.1383977226938+1.05783851828495j","0.117381277698458+0.955208098675396j","0.0405998433861358+0.90106147424607j","-0.0468210920613676+0.918458328952463j","-0.0848893724481631+1.00005925208181j","-0.0256775493469539+1.0709920984026j","0.0540993408786622+1.03275758150598j","0.0306414953961159+0.958488015724249j","-0.0367699840419155+0.976306679089002j","-0.0097447156465746+1.03625482985305j","0.0292107892383535+0.991816445841316j","-0.0210445458522367+0.986952522344235j","0.00987159056454921+1.01783265014524j","-0.00454827275067146+0.984570053304573j","0.00542547671267313+1.01175558074983j"]
[{"$nulls":15},"Mass term for slotted panel",{"$f":"IMPRODUCT(\"j\",IMSUB(IMPRODUCT(Q20,slotted_acousticMass),IMPRODUCT(airImpedance,Q27)))","v":"-28805.3557126707j"},"-25711.8183993328j","-22773.9560166937j","-20436.0799909914j","-18154.7945440827j","-16180.5212119622j","-14354.8056609469j","-12802.2922829435j","-11399.6350370015j","-10092.2690412281j","-9001.56722885694j","-7968.3218764352j","-7081.6572204197j","-6270.49284967019j","-5560.82727211726j","-4910.55642180748j","-4337.14366764265j","-3822.93625180842j","-3349.32762383839j","-2926.22275887471j","-2539.11273528393j","-2188.20569610442j","-1864.43670580344j","-1567.76218822027j","-1291.58332150252j","-1033.26449747903j","-786.796889241943j","-552.277715168276j","-324.857138082265j","-100.819441862254j","121.010129212589j","344.843103886876j",{"$f":"IMPRODUCT(\"j\",IMSUB(IMPRODUCT(AW20,slotted_acousticMass),IMPRODUCT(airImpedance,AW27)))","v":"573.422839055965j"},"809.372741259773j","1057.34206424437j","1319.56230971857j","1599.67765875673j","1902.51667442318j","2232.28344493191j","2594.0164360203j","2994.39479140725j","3440.53464483444j","3944.1108650462j","4521.73944889021j","5206.62668012355j","6100.00206587815j","7862.42699915912j","3625.874807167j","6956.90419843437j"]
[]
[{"$nulls":15},"Absorber against panel"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":14},"Eq 6.22","At top of air layer (z1)",{"$f":"IMPRODUCT(airImpedance,\"-j\",Q28)","v":"-14457.9163262228j"},"-12907.9587035707j","-11436.3613851428j","-10265.6564836456j","-9123.717678054j","-8135.93803071626j","-7223.04585011324j","-6447.35710201024j","-5747.2068209067j","-5095.42364121389j","-4552.48988114843j","-4039.14169184465j","-3599.68862019472j","-3198.86931630198j","-2849.52856896417j","-2530.93603656216j","-2251.65565273139j","-2003.02574601785j","-1776.097887659j","-1575.64353947965j","-1394.76643587206j","-1233.56417531926j","-1087.864771705j","-957.632555416437j","-839.921119785756j","-733.571094076253j","-636.097167151285j","-547.487171082149j","-465.78564729844j","-389.554769065644j","-318.189423761049j","-250.001700965923j",{"$f":"IMPRODUCT(airImpedance,\"-j\",AW28)","v":"-183.667028310227j"},"-117.612572548099j","-49.1836895819355j","24.65190605638j","109.549436034045j","216.915729650091j","373.572429460053j","668.667744859385j","1713.37713127199j","-3468.5915910763j","-725.50977925004j","-285.610959780726j","-42.2219019000304j","206.497996871361j","805.890462363121j","-1709.65186604192j","-244.934662983726j"]
[{"$nulls":14},"Eq 6.23","At top of porous absorber (z2)",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",Q35,Q24,Q29),IMPRODUCT(Q24,Q24)),IMSUB(Q35,IMPRODUCT(\"j\",Q24,Q29)))","v":"8.88233341887017-6795.54605792518j"},"54.0315393307776-6035.0158385803j","94.3967421643076-5316.60933720271j","124.527460714541-4747.89273654464j","151.99121753429-4195.75242523687j","174.006967461908-3720.38104967989j","192.723335753945-3283.01009929634j","207.236869237654-2912.92249381611j","219.105780840331-2580.12248537904j","228.98550757927-2271.36019824403j","236.26853080761-2014.87888812728j","242.298973539252-1772.8738001028j","246.767218690342-1565.95672074805j","250.281396764938-1377.25547766573j","252.938457767118-1212.59866908542j","255.103036926456-1062.02221179082j","256.911113198672-929.40927712762j","258.613085275652-810.534745658321j","260.47243234826-700.979379852396j","262.662345096766-602.9329836305j","265.483270653363-512.947770863106j","269.196129326725-430.996217019002j","274.214016313767-354.89322999344j","280.935125710066-284.56811274631j","290.024062973564-218.410150344686j","302.311846186998-155.760338188592j","319.240091024453-95.1912686208615j","342.545410050257-36.9436541482945j","375.423587653878+19.4637135951931j","423.06318982065+72.8495973285533j","493.01023114672+117.584798034964j","596.12328502509+138.074540423113j",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",AW35,AW24,AW29),IMPRODUCT(AW24,AW24)),IMSUB(AW35,IMPRODUCT(\"j\",AW24,AW29)))","v":"733.259055088979+92.6481052189819j"},"837.365552790747-82.3571724715357j","742.976636359344-319.722441107436j","502.479650518521-376.810944588486j","335.420400932032-269.135050172163j","277.140360170384-117.744945326827j","312.292199966398+35.1564834980513j","484.329216525326+137.492745894318j","668.577491687562-87.193961085086j","421.175902846868-197.558573536045j","343.614110469429-36.1533206899916j","479.433635072608+59.7221584319126j","515.185878312295-138.77136284814j","346.031940593776-48.3413866280406j","514.49236173129+31.4924966855659j","385.271940391411-85.5842009294937j","483.032372677986+17.074592845126j"]
[{"$nulls":14},"Eq 6.1","Impedance at surface of device (z3)",{"$f":"IMSUM(slotted_R1,Q31,Q36)","v":"90.5655017357018-35600.9017705959j"},"135.714707647609-31746.8342379131j","176.079910481139-28090.5653538964j","206.210629031373-25183.972727536j","233.674385851122-22350.5469693196j","255.69013577874-19900.9022616421j","274.406504070777-17637.8157602432j","288.920037554486-15715.2147767596j","300.788949157163-13979.7575223805j","310.668675896102-12363.6292394721j","317.951699124442-11016.4461169842j","323.982141856084-9741.195676538j","328.450387007174-8647.61394116775j","331.96456508177-7647.74832733592j","334.62162608395-6773.42594120268j","336.786205243288-5972.5786335983j","338.594281515504-5266.55294477027j","340.296253592484-4633.47099746674j","342.155600665092-4050.30700369079j","344.345513413598-3529.15574250521j","347.166438970195-3052.06050614704j","350.879297643557-2619.20191312342j","355.897184630599-2219.32993579688j","362.618294026898-1852.33030096658j","371.707231290396-1509.99347184721j","383.99501450383-1189.02483566762j","400.923259341285-881.988157862804j","424.228578367089-589.221369316571j","457.10675597071-305.393424487072j","504.746358137482-27.9698445337007j","574.693399463552+238.594927247553j","677.806453341922+482.917644309989j",{"$f":"IMSUM(slotted_R1,AW31,AW36)","v":"814.942223405811+666.070944274947j"},"919.048721107579+727.015568788237j","824.659804676176+737.619623136934j","584.162818835353+942.751365130084j","417.103569248864+1330.54260858457j","358.823528487216+1784.77172909635j","393.97536828323+2267.43992842996j","566.012384842158+2731.50918191462j","750.260660004394+2907.20083032216j","502.8590711637+3242.97607129839j","425.297278786261+3907.95754435621j","561.11680338944+4581.46160732212j","596.869046629127+5067.85531727541j","427.715108910608+6051.66067925011j","596.175530048122+7893.91949584469j","466.955108708243+3540.29060623751j","564.715540994818+6973.9787912795j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q37,airImpedance),IMSUM(Q37,airImpedance))","v":"0.999671200811709-0.0232235448700953j"},"0.999549529742202-0.0260403121861185j","0.999382429259845-0.0294255657107016j","0.999192514319747-0.032816287195481j","0.998929617195473-0.036967872565089j","0.998604364794114-0.0415062065653793j","0.998174260145104-0.0468135618481054j","0.997652805604233-0.0525157452189652j","0.996985590689504-0.0589990054882492j","0.996095903665976-0.066656621153582j","0.995038047671495-0.0747351338651819j","0.993609933616797-0.0844077575855157j","0.991855627037376-0.09492819364678j","0.989559682437603-0.107111561848024j","0.986678582818228-0.120615357868016j","0.982877613891889-0.136306057868628j","0.978025805225269-0.153880311271763j","0.971714892970646-0.173870612204251j","0.963191318552504-0.197301388418114j","0.951902472882567-0.223990029167026j","0.936423186586939-0.255101715615725j","0.915094257976946-0.290946265820076j","0.884686365192984-0.332634660519903j","0.840884319722088-0.379768480015898j","0.775839563676927-0.431087062851479j","0.678269723264057-0.479700193901316j","0.532690284605367-0.506095057560023j","0.339578445509467-0.464526707216891j","0.154201596360362-0.296700488645699j","0.100238105161866-0.0274076293644421j","0.209251737784739+0.190927997918526j","0.366316923301219+0.280420287000315j",{"$f":"IMDIV(IMSUB(AW37,airImpedance),IMSUM(AW37,airImpedance))","v":"0.479768726183339+0.28207977969946j"},"0.521769543179219+0.260919675745356j","0.507058060988129+0.293671092697968j","0.562120632872404+0.413789879784212j","0.72081923181327+0.447234095798311j","0.831128685007102+0.390260682043474j","0.884742735317572+0.32366045633366j","0.903808945296203+0.268249945510125j","0.901862722792176+0.245163410220821j","0.933275937491926+0.236142200719058j","0.956582951006263+0.202286732208548j","0.963265919660221+0.172683806049928j","0.968712614371382+0.15693698293507j","0.981365868861752+0.134057428360824j","0.986817006397053+0.10307106434683j","0.94529450612436+0.219976473699735j","0.983689154880691+0.11628796396889j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q39),2)","v":{"v":1.1815723134267486E-4,"d":"0.00"}},{"v":2.2263973339198273E-4,"d":"0.00"},{"v":3.6889616929625113E-4,"d":"0.00"},{"v":5.3741062208600976E-4,"d":"0.00"},{"v":7.7299628771709816E-4,"d":"0.00"},{"v":1.066557430696502E-3,"d":"0.00"},{"v":1.4566368108678285E-3,"d":"0.00"},{"v":1.9309759740991916E-3,"d":"0.00"},{"v":2.53884930889825E-3,"d":"0.00"},{"v":0.003349845556250508,"d":"0.00"},{"v":0.004313943452253222,"d":"0.00"},{"v":5.6146302774092716E-3,"d":"0.01"},{"v":0.007211053165253278,"d":"0.01"},{"v":0.009298748212467345,"d":"0.01"},{"v":0.011917309654183472,"d":"0.01"},{"v":0.015372254698501009,"d":"0.02"},{"v":0.019786374116369188,"d":"0.02"},{"v":0.02553917699076491,"d":"0.03"},{"v":0.03333464599337299,"d":"0.03"},{"v":0.043710148953808314,"d":"0.04"},{"v":0.05803473031227657,"d":"0.06"},{"v":0.07795276942297658,"d":"0.08"},{"v":0.10668421786243487,"d":"0.11"},{"v":0.1486894624319357,"d":"0.15"},{"v":0.2122369156756806,"d":"0.21"},{"v":0.3098379064743393,"d":"0.31"},{"v":0.4601088534003699,"d":"0.46"},{"v":0.6689014176276067,"d":"0.67"},{"v":0.8881906877173195,"d":"0.89"},{"v":0.9892011441261801,"d":"0.99"},{"v":0.9197602098448902,"d":"0.92"},{"v":0.7871763743417898,"d":"0.79"},{"$f":"1-POWER(IMABS(AW39),2)","v":{"v":0.6902529672611204,"d":"0.69"}},{"v":0.6596774666194875,"d":"0.66"},{"v":0.6566494121005404,"d":"0.66"},{"v":0.5127983294872954,"d":"0.51"},{"v":0.2804012986035944,"d":"0.28"},{"v":0.1569217090093279,"d":"0.16"},{"v":0.1124742013086677,"d":"0.11"},{"v":0.11117135713637982,"d":"0.11"},{"v":0.12653853152678018,"d":"0.13"},{"v":0.07323288553812679,"d":"0.07"},{"v":0.044029135816536336,"d":"0.04"},{"v":0.04229907114925935,"d":"0.04"},{"v":0.036966654144999556,"d":"0.04"},{"v":0.018949637334501057,"d":"0.02"},{"v":0.015568551579970058,"d":"0.02"},{"v":0.05802864770973215,"d":"0.06"},{"v":0.01883275600608203,"d":"0.02"}]
[]
[{"$nulls":15},"Absorber against backing"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":14},"Eq 6.22","At top of porous absorber (z1)",{"$f":"IMPRODUCT(\"-j\",Q29,Q24)","v":"-836.495183532115-12788.9760719444j"},"-644.183328734355-11321.2938783704j","-471.875113042972-9941.97799853962j","-342.806305970193-8855.62045262786j","-224.584425400221-7806.30707327311j","-129.178825062794-6907.75034362523j","-47.3803516898633-6085.60760858231j","16.7025715067903-5393.91002771144j","69.7202563028964-4775.51701398921j","114.430158917455-4205.3702681801j","147.81233638988-3734.84902635878j","175.726563859238-3293.93811909865j","196.446957194337-2919.76546076842j","212.467734014234-2581.26544586543j","223.920485456422-2288.48980566054j","232.090018121537-2023.35163124503j","237.275530689448-1792.39268691264j","240.191322458355-1587.89103867817j","241.34576123182-1402.07733702953j","241.10553436639-1238.50231633258j","239.85689742301-1091.22534621742j","237.951583153105-960.077250971181j","235.673909541489-841.463215463903j","233.336881598601-735.200944287097j","231.191011937461-638.776395695408j","229.509256893658-551.166212844586j","228.557452878235-470.278497594895j","228.658022098446-396.095845438649j","230.166536273952-327.018665933466j","233.557816521097-261.90664478536j","239.415626918912-200.396456261531j","248.623688335783-141.315747106563j",{"$f":"IMPRODUCT(\"-j\",AW29,AW24)","v":"262.448398468025-84.0388495381044j"},"282.788503181253-28.2261270869587j","312.845782913978+26.2449767491055j","357.311936714538+77.1637150243177j","423.027709388796+118.062027561858j","516.283908508859+131.442139232291j","624.600241624742+81.1478164557899j","677.479211546699-56.0894299071111j","597.035044498603-191.575347430087j","457.863413805763-211.998499721736j","364.274447253147-144.661880702539j","338.583462135046-49.4477608735237j","381.963774933298+36.3027035605962j","491.010390102848+49.6801641484357j","530.015802765189-72.9534564770556j","412.585572321087-108.72487276605j","372.062395057155-14.6539463224877j"]
[{"$nulls":14},"Eq 6.23","At top of air layer (z2)",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",Q44,airImpedance,Q28),airImpedance^2),IMSUB(Q44,IMPRODUCT(\"j\",airImpedance,Q28)))","v":"-235.497778014657-6787.12186871176j"},"-182.887106711178-6029.14376871095j","-135.148319550256-5313.4560599437j","-98.9356645145598-4747.15753216595j","-65.3465599493593-4197.64644499672j","-37.8779208266979-3724.81541129447j","-14.0018707102454-3290.06438395873j","4.972010532557-2922.45646836455j","20.9044743387384-2592.14081792825j","34.5657211414724-2285.9488339795j","44.9581130122121-2031.84019605407j","53.841938685688-1792.31443427456j","60.6248961406022-1587.73978577822j","66.0723092250072-1401.38767448923j","70.1897089585895-1238.97465468651j","73.399035321302-1090.63143363994j","75.7765289800665-960.144702085127j","77.5716793405511-843.310888253414j","79.00262498827-735.747379153879j","80.200141826106-639.56010469413j","81.3790556698351-551.31492039355j","82.7259280361006-470.925741215846j","84.4922447483683-396.174915967894j","86.9396137216925-326.895187405567j","90.4564405987236-261.361802744553j","95.5492401480947-198.709558957107j","103.073183710185-137.151887928146j","114.179817503887-76.3113267475622j","131.009848845912-14.5246824235325j","157.368835289771+49.3931773615723j","199.753720077209+114.48683905077j","270.042472778139+175.02751497913j",{"$f":"IMDIV(IMSUM(IMPRODUCT(\"-j\",AW44,airImpedance,AW28),airImpedance^2),IMSUB(AW44,IMPRODUCT(\"j\",airImpedance,AW28)))","v":"382.234367093413+206.224422290528j"},"516.179350591534+148.589640136935j","551.234380087286-8.76566946151685j","444.101557118518-101.89431648712j","335.402881537223-70.9151979996725j","290.16593926542+21.1289027534283j","324.928067449502+137.018933497165j","501.940121849636+214.812292457221j","694.061117366359-55.7375232797493j","406.130704618789-203.86110177175j","285.446476855924-43.6408299830002j","376.828345128877+87.2945047359679j","452.138866621308-35.2152174861331j","341.943069534773+28.0937339625174j","531.509413999047+70.8880030698365j","367.152199034236-91.5123499890286j","417.501255180292+46.3567216218104j"]
[{"$nulls":14},"Eq 6.1","Impedance at surface of device (z3)",{"$f":"IMSUM(slotted_R0,Q31,Q45)","v":"177.002221985343-35592.4775813825j"},"229.612893288822-31740.9621680437j","277.351680449744-28087.4120766374j","313.56433548544-25183.2375231573j","347.153440050641-22352.4409890794j","374.622079173302-19905.3366232567j","398.498129289755-17644.8700449056j","417.472010532557-15724.748751308j","433.404474338738-13991.7758549298j","447.065721141472-12378.2178752076j","457.458113012212-11033.407424911j","466.341938685688-9760.63631070976j","473.124896140602-8669.39700619792j","478.572309225007-7671.88052415942j","482.68970895859-6799.80192680377j","485.899035321302-6001.18785544742j","488.276528980066-5297.28836972778j","490.071679340551-4666.24714006183j","491.50262498827-4085.07500299227j","492.700141826106-3565.78286356884j","493.879055669835-3090.42765567748j","495.225928036101-2659.13143732027j","496.992244748368-2260.61162177133j","499.439613721692-1894.65737562584j","502.956440598724-1552.94512424707j","508.049240148095-1231.97405643614j","515.573183710185-923.948777170089j","526.679817503887-628.589041915838j","543.509848845912-339.381820505798j","569.868835289771-51.4262645006817j","612.253720077209+235.496968263359j","682.542472778139+519.870618866006j",{"$f":"IMSUM(slotted_R0,AW31,AW45)","v":"794.734367093413+779.647261346493j"},"928.679350591534+957.962381396708j","963.734380087286+1048.57639478285j","856.601557118518+1217.66799323145j","747.902881537223+1528.76246075706j","702.66593926542+1923.64557717661j","737.428067449502+2369.30237842907j","914.440121849636+2808.82872847752j","1106.56111736636+2938.6572681275j","818.630704618789+3236.67354306269j","697.946476855924+3900.4700350632j","789.328345128877+4609.03395362618j","864.638866621308+5171.41146263742j","754.443069534773+6128.09579984067j","944.009413999047+7933.31500222896j","779.652199034236+3534.36245717797j","830.001255180292+7003.26092005618j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q46,airImpedance),IMSUM(Q46,airImpedance))","v":"0.999614661976789-0.0232273050596847j"},"0.999472373321658-0.0260422338049543j","0.999276301036947-0.0294240322319256j","0.999052786263966-0.0328097690765655j","0.998742537238059-0.0369529398888056j","0.998357764003626-0.04147885792634j","0.997847906067323-0.0467669882480015j","0.99722878588016-0.0524423095729669j","0.996435791985665-0.0588864794597871j","0.995377930013634-0.0664851279618373j","0.994120462875167-0.074485076714609j","0.992424750500624-0.0840396084287002j","0.990346014289828-0.0943993761519275j","0.987634055204788-0.106351224883754j","0.984245957059759-0.119536818693483j","0.979802620626236-0.134769972158411j","0.97417448391672-0.151710965785613j","0.966924623554766-0.170813885625538j","0.957252968823288-0.192960929562762j","0.94463968776893-0.217842448619523j","0.927672305796481-0.246347208454685j","0.904840979664302-0.278464618444528j","0.873233761771439-0.31475052052215j","0.829322881769893-0.354223237494088j","0.766925815090497-0.394958549739128j","0.678048261595971-0.430414390123899j","0.552500974887156-0.445043999336331j","0.392144071219469-0.406414573275056j","0.232419650298714-0.272212789388764j","0.161339662452569-0.0438598172525989j","0.234164244670977+0.175828604879723j","0.38407394178979+0.292151009288914j",{"$f":"IMDIV(IMSUB(AW46,airImpedance),IMSUM(AW46,airImpedance))","v":"0.516776031965635+0.311820992166119j"},"0.59181328586532+0.291343737250272j","0.619895233930643+0.289403800010221j","0.66074034069765+0.325261072651486j","0.739441803219632+0.342982655935229j","0.813394291039282+0.321611778149836j","0.862826675011401+0.282391992089277j","0.886240008894326+0.240627539733546j","0.885167184745623+0.222004499163927j","0.9150516923215+0.223154970951874j","0.944125070377031+0.196090319032666j","0.956163363833338+0.167978395174874j","0.962754161553278+0.150701707953341j","0.975183410369782+0.130213562785531j","0.982671219212493+0.101271834203688j","0.929095972276691+0.210037180374876j","0.979674920677257+0.114471126342836j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q48),2)","v":{"v":2.310198606938485E-4,"d":"0.00"}},{"v":3.7677702522076473E-4,"d":"0.00"},{"v":5.811005131314273E-4,"d":"0.00"},{"v":8.170493113487387E-4,"d":"0.00"},{"v":1.1478245448587332E-3,"d":"0.00"},{"v":1.5612793988066809E-3,"d":"0.00"},{"v":2.1124051672702926E-3,"d":"0.00"},{"v":2.7845527786350965E-3,"d":"0.00"},{"v":0.003648094986732464,"d":"0.00"},{"v":0.004802504201671609,"d":"0.00"},{"v":6.1764786396827365E-3,"d":"0.01"},{"v":0.008030458808925056,"d":"0.01"},{"v":0.010303529762378583,"d":"0.01"},{"v":0.013268389965471084,"d":"0.01"},{"v":0.016970844988160483,"d":"0.02"},{"v":0.021823879218381692,"d":"0.02"},{"v":0.027967857745988645,"d":"0.03"},{"v":0.03587938884097963,"d":"0.04"},{"v":0.046432833341276125,"d":"0.05"},{"v":0.06020052787126895,"d":"0.06"},{"v":0.07873714594482428,"d":"0.08"},{"v":0.10372025779468952,"d":"0.10"},{"v":0.1383949071335373,"d":"0.14"},{"v":0.18674945579208702,"d":"0.19"},{"v":0.2558325381357419,"d":"0.26"},{"v":0.3549940077209538,"d":"0.35"},{"v":0.4966785114034661,"d":"0.50"},{"v":0.6810502220370742,"d":"0.68"},{"v":0.8718813034482119,"d":"0.87"},{"v":0.9720458297502598,"d":"0.97"},{"v":0.9142514082237211,"d":"0.91"},{"v":0.7671349950095219,"d":"0.77"},{"$f":"1-POWER(IMABS(AW48),2)","v":{"v":0.63571020163039,"d":"0.64"}},{"v":0.5648758614383376,"d":"0.56"},{"v":0.5319753394897172,"d":"0.53"},{"v":0.45762743679235807,"d":"0.46"},{"v":0.33558871737891527,"d":"0.34"},{"v":0.23495559146000478,"d":"0.23"},{"v":0.17578489169262013,"d":"0.18"},{"v":0.15667703375676578,"d":"0.16"},{"v":0.16719305740048207,"d":"0.17"},{"v":0.11288225931902729,"d":"0.11"},{"v":0.07017643826723374,"d":"0.07"},{"v":0.05753488041738941,"d":"0.06"},{"v":0.05039341963179067,"d":"0.05"},{"v":0.03206174420625996,"d":"0.03"},{"v":0.024101290528453556,"d":"0.02"},{"v":0.09266505715940199,"d":"0.09"},{"v":0.027133411029812926,"d":"0.03"}]
[]
[{"$nulls":15},"No air gap"]
[{"$nulls":15},"Impedence values"]
[{"$nulls":14},"Eq 6.25","At top of porous layer (z1)",{"$f":"IMPRODUCT(\"-j\",Q30,Q24)","v":"-158.635510416822-6387.78960287074j"},"-69.2453329141554-5651.73349995166j","10.2409968917732-4959.54449167996j","69.3000015685298-4413.95879952564j","122.933157764751-3886.50863132638j","165.808116657782-3434.34475181998j","202.204769738929-3020.09007117333j","230.433173301568-2671.01710820903j","253.567176746076-2358.36409067124j","272.914881632401-2069.45052077553j","287.288129172098-1830.37875499299j","299.32474575514-1605.63293244695j","308.382366597436-1414.16500172459j","315.64209185067-1240.15354637429j","321.242703831751-1088.82064897139j","325.873380700145-950.878764934412j","329.734950659001-829.788627529729j","333.266176109076-721.605224197674j","336.913585502345-622.270666515319j","340.927197464468-533.761139747927j","345.78159144381-452.985760615573j","351.85159003327-379.997164641824j","359.728195174183-313.000856684191j","369.920508145684-252.195046596183j","383.247458238369-196.612258432749j","400.577744744046-146.408144163993j","423.23840364648-101.643728623816j","452.108607095555-64.4291057591437j","488.113400097631-37.4563493360096j","530.479659963598-25.8599396178138j","573.406515911812-36.4967925073049j","603.599630202922-73.325907775354j",{"$f":"IMPRODUCT(\"-j\",AW30,AW24)","v":"601.774922996656-127.160374528719j"},"560.328898209479-170.591625035024j","498.089189845152-178.048193602809j","445.891709391728-148.270276989255j","422.799370323731-99.0414861710878j","433.861742446488-52.8472837298541j","470.039103260695-35.4502727710193j","493.860234318888-61.8237506250233j","467.145522360808-89.8849107877039j","431.575244358215-69.4919199335324j","440.222974431616-35.5701650595105j","462.586722157636-46.4449302324531j","438.291649241386-57.6201136102735j","435.870846524044-31.5719141417366j","445.919562135028-43.0391800613373j","429.815700548369-32.4247407338319j","439.411313072831-34.8490684735718j"]
[{"$nulls":14},"Eq 6.1","Impedance at surface of device (z2)",{"$f":"IMSUM(slotted_R1,Q31,Q53)","v":"-76.9523420999903-35193.1453155414j"},"12.4378354026763-31363.5518992845j","91.9241652086049-27733.5005083737j","150.983169885361-24850.038790517j","204.616326081583-22041.3031754091j","247.491284974614-19614.8659637822j","283.887938055761-17374.8957321202j","312.1163416184-15473.3093911525j","335.250345062908-13757.9991276727j","354.598049949233-12161.7195620036j","368.97129748893-10831.9459838499j","381.007914071972-9573.95480888215j","390.065534914268-8495.82222214429j","397.325260167502-7510.64639604448j","402.925872148583-6649.64792108865j","407.556549016977-5861.43518674189j","411.418118975833-5166.93229517238j","414.949344425908-4544.54147600609j","418.596753819177-3971.59829035371j","422.6103657813-3459.98389862264j","427.464759760642-2992.0984958995j","433.534758350102-2568.20286074624j","441.411363491015-2177.43756248763j","451.603676462516-1819.95723481645j","464.930626555201-1488.19557993527j","482.260913060878-1179.67264164302j","504.921571963312-888.440617865759j","533.791775412387-616.70682092742j","569.796568414463-362.313487418275j","612.16282828043-126.679381480068j","655.089684228644+84.5133367052841j","685.282798519754+271.517196111522j",{"$f":"IMSUM(slotted_R1,AW31,AW53)","v":"683.458091313488+446.262464527246j"},"642.012066526311+638.781116224749j","579.772358161984+879.293870641561j","527.57487770856+1171.29203272931j","504.482538640563+1500.63617258564j","515.54491076332+1849.66939069333j","551.722271577527+2196.83317216089j","575.54340263572+2532.19268539528j","548.82869067764+2904.50988061955j","513.258412675047+3371.04272490091j","521.906142748448+3908.54069998669j","544.269890474468+4475.29451865776j","519.974817558218+5149.00656651328j","517.554014840876+6068.43015173641j","527.60273045186+7819.38781909778j","511.498868865201+3593.45006643317j","521.094481389663+6922.0551299608j"]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q54,airImpedance),IMSUM(Q54,airImpedance))","v":"0.999775336934161-0.0234951794134939j"},"0.999642015597056-0.0263615677322186j","0.999456805591353-0.0298076450209774j","0.999244510927377-0.033260246950775j","0.998948736749658-0.0374884863374484j","0.99858097309954-0.0421112712764758j","0.998092825806724-0.0475176882770571j","0.997499385468845-0.0533260486335531j","0.996738610071431-0.0599289898457432j","0.995722806350046-0.0677255939471064j","0.994513991208787-0.0759468681794673j","0.992881367833239-0.0857836985849782j","0.990875597348087-0.0964724827743286j","0.988250957376511-0.108834676429198j","0.984958748777927-0.122512533686705j","0.980618447103371-0.138367485855669j","0.975084077244814-0.156067839018589j","0.967896590907521-0.176112311426316j","0.958212183878632-0.199459878576947j","0.945432846160036-0.225816717970953j","0.928010246167206-0.25614330760492j","0.90422263014954-0.290405698580658j","0.870808857280371-0.329057174667362j","0.823826510799041-0.370635846454527j","0.756760366197676-0.412098004163829j","0.662382110351145-0.444639679083578j","0.534864544590213-0.449965079202021j","0.386887349567458-0.399160814872229j","0.259523354712357-0.272849723921443j","0.20583952576563-0.0980892149708026j","0.230925195376498+0.0608266724394077j","0.290694075982846+0.175279034007289j",{"$f":"IMDIV(IMSUB(AW54,airImpedance),IMSUM(AW54,airImpedance))","v":"0.353182621112811+0.263143664141362j"},"0.426559433272662+0.347047261520482j","0.533237493066614+0.413212749613867j","0.655284188819636+0.429056943676643j","0.754698392287909+0.401009283579526j","0.820685492631913+0.35701438476164j","0.86137415593371+0.315519605701912j","0.889330888496266+0.283347853914125j","0.915001828462806+0.256549662956966j","0.937300955610782+0.228071784083441j","0.952109674113355+0.200112866193054j","0.962187634011968+0.176687894031837j","0.971811243691236+0.155492547838206j","0.979574069604437+0.133136209088334j","0.987453865167043+0.104245758096794j","0.944445454887359+0.215825597313873j","0.984159400789793+0.117326538400506j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q56),2)","v":{"v":-1.027477974875346E-4,"d":"-0.00"}},{"v":2.0908399754659968E-5,"d":"0.00"},{"v":1.9759805543184683E-4,"d":"0.00"},{"v":4.0416335428083983E-4,"d":"0.00"},{"v":6.9603473838930618E-4,"d":"0.00"},{"v":1.0626809950546878E-3,"d":"0.00"},{"v":0.001552780373953011,"d":"0.00"},{"v":2.1513085264086573E-3,"d":"0.00"},{"v":2.9206593689404814E-3,"d":"0.00"},{"v":0.003949336838900641,"d":"0.00"},{"v":0.005173994503699486,"d":"0.01"},{"v":0.006827746466677942,"d":"0.01"},{"v":0.008858610647428877,"d":"0.01"},{"v":0.011515058450961013,"d":"0.01"},{"v":0.014846942295484444,"d":"0.01"},{"v":0.019241900058554307,"d":"0.02"},{"v":0.024853871927697613,"d":"0.02"},{"v":0.03216064307367883,"d":"0.03"},{"v":0.04204516750461218,"d":"0.04"},{"v":0.0551635432865607,"d":"0.06"},{"v":0.07318758897789335,"d":"0.07"},{"v":0.09804596535732812,"d":"0.10"},{"v":0.13341330988198785,"d":"0.13"},{"v":0.1839389494276139,"d":"0.18"},{"v":0.257488983116548,"d":"0.26"},{"v":0.3635454956712162,"d":"0.36"},{"v":0.5114513464390229,"d":"0.51"},{"v":0.6909888226152057,"d":"0.69"},{"v":0.8582006565148365,"d":"0.86"},{"v":0.9480085955389922,"d":"0.95"},{"v":0.9429736700602752,"d":"0.94"},{"v":0.8847742144259509,"d":"0.88"},{"$f":"1-POWER(IMABS(AW56),2)","v":{"v":0.8060174481661426,"d":"0.81"}},{"v":0.6976052481572397,"d":"0.70"},{"v":0.5449129995445805,"d":"0.54"},{"v":0.3865127709658496,"d":"0.39"},{"v":0.2696218911610806,"d":"0.27"},{"v":0.1990160512567819,"d":"0.20"},{"v":0.15848194190719855,"d":"0.16"},{"v":0.12880456444870192,"d":"0.13"},{"v":0.09695392434638905,"d":"0.10"},{"v":0.06945017991611113,"d":"0.07"},{"v":0.05344200924376186,"d":"0.05"},{"v":0.042976345057045395,"d":"0.04"},{"v":0.03140497420207644,"d":"0.03"},{"v":0.022709391988188887,"d":"0.02"},{"v":0.014067686085491804,"d":"0.01"},{"v":0.06144209428671932,"d":"0.06"},{"v":0.017664757224029937,"d":"0.02"}]

{"sheet":"Microperforated Panel","index":3,"n_rows":32,"n_cols":65,"rows_kept":32}
[]
[null,"Microperforated Panel",{"$nulls":13},"Cox & D'Antonio Chapter 6, Section 5"]
[null,"Properties of panel",{"$nulls":4},"Display options",{"$nulls":8},"Panel thickness (tp)",{"$f":"micro_panel_thickness_mm/1000","v":{"v":2.0999999999999998E-4,"d":"0.00021"}},"m"]
[null,"Panel thickness (tp)",{"v":0.21,"d":"0.2"},"mm",{"$f":"micro_panel_thickness_mm/25.4","v":{"v":0.00826771653543307,"d":"0.008"}},"in","Start graph at",62.5,"Hz",null,"Open Area (e)",{"$f":"(PI()*(micro_hole_diameter/2)^2)/(micro_repeat_distance^2)","v":{"v":0.005026548245743669,"d":"0.50%"}},{"$nulls":3},"Repeat distance (D)",{"$f":"micro_repeat_distance_mm/1000","v":{"v":0.0025,"d":"0.00250"}},"m",null,"cos(y)",{"$f":"COS(microPerfAbsAngle*PI()/180)","v":{"v":0.9396926207859084,"d":"0.9397"}}]
[null,"Repeat distance (D)",2.5,"mm",{"$f":"micro_repeat_distance_mm/25.4","v":{"v":0.0984251968503937,"d":"0.098"}},"in",{"$nulls":4},"To see the graph in the standard",{"$nulls":4},"Hole diameter (a)",{"$f":"micro_hole_diameter_mm/1000","v":{"v":0.0002,"d":"0.00020"}},"m",null,"Hole radius",{"$f":"micro_hole_diameter/2","v":1E-4},"m"]
[null,"Hole diameter (2a)",{"v":0.2,"d":"0.20"},"mm",{"$f":"micro_hole_diameter_mm/25.4","v":{"v":0.007874015748031498,"d":"0.008"}},"in",{"$nulls":4},"analysis frequencies, select",{"$nulls":4},"Cavity depth (d)",{"$f":"micro_cavity_depth_mm/1000","v":{"v":0.065,"d":"0.06500"}},"m"]
[null,"Properties of cavity",{"$nulls":4},"Show subdivisions of",{"$nulls":3},"Whole Octaves and set the",{"$nulls":4},"Octave subdivisions",6,null,null,"Principal root of -j",{"$f":"IMSQRT(\"-j\")","v":"0.707106781186548-0.707106781186547j"}]
[null,"Cavity depth (d)",{"v":65,"d":"65.0"},"mm",{"$f":"micro_cavity_depth_mm/25.4","v":{"v":2.5590551181102366,"d":"2.559"}},"in",{"$nulls":4},"starting frequency to 62.5Hz"]
[null,"Properties of incident sound"]
[null,"Angle of incidence (y)",20,"°",null,{"$f":"IF(microPerfAbsAngle=0,\"Normal incidence\",\"Oblique incidence\")","v":"Oblique incidence"},{"$nulls":9},"Interval number",0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]
[null,"When the perforations in a membrane are sub-millimetre in diameter, then the resistance caused by the viscous air/membrane boundary layer becomes significant.",{"$nulls":13},"Angular values",{"$f":"start_freq_micro","v":62.5},{"$f":"ROUND(POWER(2,LOG(start_freq_micro,2)+R10/subdiv_micro),0)","v":70},79,88,99,111,125,140,157,177,198,223,250,281,315,354,397,445,500,561,630,707,794,891,{"v":1000,"d":"1,000"},{"v":1122,"d":"1,122"},{"v":1260,"d":"1,260"},{"v":1414,"d":"1,414"},{"v":1587,"d":"1,587"},{"v":1782,"d":"1,782"},{"v":2000,"d":"2,000"},{"v":2245,"d":"2,245"},{"v":2520,"d":"2,520"},{"v":2828,"d":"2,828"},{"v":3175,"d":"3,175"},{"v":3564,"d":"3,564"},{"v":4000,"d":"4,000"},{"v":4490,"d":"4,490"},{"v":5040,"d":"5,040"},{"v":5657,"d":"5,657"},{"v":6350,"d":"6,350"},{"v":7127,"d":"7,127"},{"v":8000,"d":"8,000"},{"v":8980,"d":"8,980"},{"v":10079,"d":"10,079"},{"v":11314,"d":"11,314"},{"v":12699,"d":"12,699"},{"v":14254,"d":"14,254"},{"v":16000,"d":"16,000"}]
[null,"Hence, a microperforated panel does not require a seperate absorbent layer, since this role is performed by the viscous boundary layer within the holes.",{"$nulls":12},"2pf","Angular frequency (w)",{"$f":"2*PI()*Q11","v":{"v":392.6990816987241,"d":"392.70"}},{"v":439.822971502571,"d":"439.82"},{"v":496.37163926718733,"d":"496.37"},{"v":552.9203070318035,"d":"552.92"},{"v":622.0353454107791,"d":"622.04"},{"v":697.4335690969341,"d":"697.43"},{"v":785.3981633974482,"d":"785.40"},{"v":879.645943005142,"d":"879.65"},{"v":986.460093227195,"d":"986.46"},{"v":1112.1237993707869,"d":"1112.12"},{"v":1244.0706908215582,"d":"1244.07"},{"v":1401.1503235010478,"d":"1401.15"},{"v":1570.7963267948965,"d":"1570.80"},{"v":1765.5750713174637,"d":"1765.58"},{"v":1979.2033717615698,"d":"1979.20"},{"v":2224.2475987415737,"d":"2224.25"},{"v":2494.4245669502957,"d":"2494.42"},{"v":2796.0174616949157,"d":"2796.02"},{"v":3141.592653589793,"d":"3141.59"},{"v":3524.866957327748,"d":"3524.87"},{"v":3958.4067435231395,"d":"3958.41"},{"v":4442.212012175967,"d":"4442.21"},{"v":4988.849133900591,"d":"4988.85"},{"v":5598.318108697012,"d":"5598.32"},{"v":6283.185307179586,"d":"6283.19"},{"v":7049.733914655496,"d":"7049.73"},{"v":7916.813487046279,"d":"7916.81"},{"v":8884.424024351934,"d":"8884.42"},{"v":9971.415082494002,"d":"9971.42"},{"v":11196.636217394023,"d":"11196.64"},{"v":12566.370614359172,"d":"12566.37"},{"v":14105.75101461817,"d":"14105.75"},{"v":15833.626974092558,"d":"15833.63"},{"v":17768.84804870387,"d":"17768.85"},{"v":19949.113350295185,"d":"19949.11"},{"v":22393.272434788047,"d":"22393.27"},{"v":25132.741228718343,"d":"25132.74"},{"v":28211.50202923634,"d":"28211.50"},{"v":31667.253948185116,"d":"31667.25"},{"v":35543.97928271492,"d":"35543.98"},{"v":39898.22670059037,"d":"39898.23"},{"v":44780.26168426891,"d":"44780.26"},{"v":50265.48245743669,"d":"50265.48"},{"v":56423.00405847268,"d":"56423.00"},{"v":63328.22471106305,"d":"63328.22"},{"v":71087.95856542984,"d":"71087.96"},{"v":79790.17021587357,"d":"79790.17"},{"v":89560.52336853782,"d":"89560.52"},{"v":100530.96491487337,"d":"100530.96"}]
[null,"This plot is a simplification of reality because it is only calculated for sound incident at exactly the specified angle.",{"$nulls":12},"2p/l","Wave number (kair)",{"$f":"TwoPiByC*Q11","v":{"v":1.1436219656127162,"d":"1.1436"}},{"v":1.2808566014862421,"d":"1.2809"},{"v":1.4455381645344731,"d":"1.4455"},{"v":1.6102197275827044,"d":"1.6102"},{"v":1.8114971935305424,"d":"1.8115"},{"v":2.031072610928184,"d":"2.0311"},{"v":2.2872439312254325,"d":"2.2872"},{"v":2.5617132029724843,"d":"2.5617"},{"v":2.872778377619143,"d":"2.8728"},{"v":3.238737406615212,"d":"3.2387"},{"v":3.622994387061085,"d":"3.6230"},{"v":4.080443173306171,"d":"4.0804"},{"v":4.574487862450865,"d":"4.5745"},{"v":5.1417243573947715,"d":"5.1417"},{"v":5.76385470668809,"d":"5.7639"},{"v":6.477474813230424,"d":"6.4775"},{"v":7.2642867255719725,"d":"7.2643"},{"v":8.142588395162539,"d":"8.1426"},{"v":9.14897572490173,"d":"9.1490"},{"v":10.26515076333974,"d":"10.2652"},{"v":11.52770941337618,"d":"11.5277"},{"v":12.936651675011046,"d":"12.9367"},{"v":14.528573451143945,"d":"14.5286"},{"v":16.30347474177488,"d":"16.3035"},{"v":18.29795144980346,"d":"18.2980"},{"v":20.53030152667948,"d":"20.5303"},{"v":23.05541882675236,"d":"23.0554"},{"v":25.87330335002209,"d":"25.8733"},{"v":29.038848950838087,"d":"29.0388"},{"v":32.60694948354976,"d":"32.6069"},{"v":36.59590289960692,"d":"36.5959"},{"v":41.07890100480876,"d":"41.0789"},{"v":46.11083765350472,"d":"46.1108"},{"v":51.74660670004418,"d":"51.7466"},{"v":58.09599585312598,"d":"58.0960"},{"v":65.21389896709952,"d":"65.2139"},{"v":73.19180579921384,"d":"73.1918"},{"v":82.15780200961753,"d":"82.1578"},{"v":92.22167530700943,"d":"92.2217"},{"v":103.51151135153816,"d":"103.5115"},{"v":116.19199170625195,"d":"116.1920"},{"v":130.40949998274925,"d":"130.4095"},{"v":146.38361159842768,"d":"146.3836"},{"v":164.31560401923505,"d":"164.3156"},{"v":184.42505266256904,"d":"184.4251"},{"v":207.02302270307632,"d":"207.0230"},{"v":232.3656854610541,"d":"232.3657"},{"v":260.8189999654985,"d":"260.8190"},{"v":292.76722319685535,"d":"292.7672"}]
[null,"In addition to this, it is assumed that the microperforated panel is perfectly rigid.  Whether or not this is actually true depends on how the panel is mounted."]
[{"$nulls":15},"Intermediate values fo Eq 6.36"]
[{"$nulls":14},"Eq 6.37","k' = a√(rw/h)",{"$f":"micro_hole_radius*SQRT(AirDensityByViscosity*Q12)","v":0.5055669320229467},0.5350417492922456,0.5683975495746263,0.5999015546230677,0.6362916859774848,0.6737521137726014,0.7149796119542078,0.7566632982849191,0.8012877023646364,0.8507956965349722,0.8998523319346016,0.9549729778324505,1.0111338640458933,1.0719926588866668,1.1349949474273784,1.2032068128484217,1.2741891560283982,1.3490208337962297,1.4299592239084156,1.51467717836169,1.6051252478767368,1.700389279607947,1.8019755854840886,1.9088750579324545,2.0222677280917867,2.1420770082561136,2.2699898948547568,2.4047135805353754,2.547575799578369,2.6995569958038046,2.859918447816831,3.0300292713706587,{"$f":"micro_hole_radius*SQRT(AirDensityByViscosity*AW12)","v":3.2102504957534737},3.400778559215894,3.6033837536347435,3.817750115864909,4.044535456183573,4.285108489959852,4.5399797897095135,4.8098523038040515,5.095954174825126,5.398735252594719,5.719836895633662,6.060058542741317,6.420182506376092,6.802158361051165,7.206483770679789,7.634964613881188,8.089070912367147]
[{"$nulls":15},"jwrt",{"$f":"IMPRODUCT(\"j\",Q12,airDensity,micro_panel_thickness)","v":"0.0992997929903543j"},{"$f":"IMPRODUCT(\"j\",R12,airDensity,micro_panel_thickness)","v":"0.111215768149197j"},"0.125514938339808j","0.139814108530419j","0.157290872096721j","0.176356432350869j","0.198599585980709j","0.222431536298394j","0.24944107999177j","0.281217013748683j","0.314581744193442j","0.354301661389584j","0.397199171961417j","0.446451869284633j","0.500470956671386j","0.562434027497367j","0.630752285074731j","0.707014526091323j","0.794398343922834j","0.89131494188142j","1.00094191334277j","1.12327925830689j","1.26150457014946j","1.41561784887049j","1.58879668784567j","1.78262988376284j","2.00188382668554j","2.24655851661378j","2.52142034361108j","2.83123569774098j","3.17759337569134j","3.56684856421353j",{"$f":"IMPRODUCT(\"j\",AW12,airDensity,micro_panel_thickness)","v":"4.00376765337109j"},"4.49311703322755j","5.04442948391j","5.66247139548196j","6.35518675138268j","7.13369712842705j","8.00753530674217j","8.98782286314295j","10.08885896782j","11.3233539942761j","12.7103735027654j","14.2673942568541j","16.0134818167965j","17.9756457262859j","20.1761291389522j","22.6467079885522j","25.4207470055307j"]
[{"$nulls":15},"k' √(-j)",{"$f":"IMPRODUCT(Q16,$U$7)","v":"0.357489805977104-0.357489805977104j"},{"$f":"IMPRODUCT(R16,$U$7)","v":"0.37833164914246-0.378331649142459j"},"0.401917761714035-0.401917761714035j","0.424194457318324-0.424194457318323j","0.449926165967301-0.4499261659673j","0.476414688487377-0.476414688487376j","0.505566932022947-0.505566932022946j","0.535041749292246-0.535041749292245j","0.566595968023423-0.566595968023422j","0.601603406424211-0.601603406424211j","0.636291685977485-0.636291685977484j","0.675267868475237-0.675267868475236j","0.714979611954208-0.714979611954207j","0.75801327848096-0.758013278480959j","0.802562623938369-0.802562623938368j","0.850795696534973-0.850795696534972j","0.900987792742045-0.900987792742044j","0.953901779539245-0.953901779539244j","1.01113386404589-1.01113386404589j","1.07103850412806-1.07103850412806j","1.13499494742738-1.13499494742738j","1.20235679026769-1.20235679026769j","1.2741891560284-1.2741891560284j","1.3497784979019-1.3497784979019j","1.42995922390842-1.42995922390841j","1.51467717836169-1.51467717836169j","1.60512524787674-1.60512524787674j","1.70038927960795-1.70038927960795j","1.80140812346861-1.8014081234686j","1.90887505793246-1.90887505793245j","2.02226772809179-2.02226772809179j","2.14255424497993-2.14255424497992j","2.26998989485476-2.26998989485476j","2.40471358053538-2.40471358053537j","2.54797708741256-2.54797708741256j","2.69955699580381-2.6995569958038j","2.85991844781683-2.85991844781683j","3.03002927137066-3.03002927137066j","3.21025049575348-3.21025049575347j","3.40107918052559-3.40107918052558j","3.60338375363475-3.60338375363474j","3.8174823069406-3.81748230694059j","4.04453545618358-4.04453545618357j","4.28510848995986-4.28510848995985j","4.53975458671378-4.53975458671378j","4.80985230380405-4.80985230380405j","5.09575354275848-5.09575354275848j","5.39873525259472-5.39873525259471j","5.71983689563367-5.71983689563366j"]
[{"$nulls":15},"Bessel, first kind, zero order (k' √(-j))",{"$f":"zbesselj(0,Q18)","v":"0.99897924+0.06389223j"},{"$f":"zbesselj(0,R18)","v":"0.99871957+0.07155724j"},"0.99836917+0.08075431j","0.99797644+0.08995024j","0.99743897+0.10118797j","0.99678055+0.11344488j","0.99591732+0.12774098j","0.99487883+0.14305338j","0.99355985+0.16040062j","0.99181493+0.18079873j","0.98975808+0.20220315j","0.98700945+0.22766419j","0.98367483+0.25513416j","0.97937764+0.28663353j","0.97408908+0.32112577j","0.96728206+0.36061017j","0.95886054+0.40403280j","0.94832624+0.45234971j","0.93478822+0.50748754j","0.91794455+0.56832476j","0.89658030+0.63669161j","0.86985253+0.71235385j","0.83600709+0.79694374j","0.79373649+0.88999632j","0.74057352+0.99278337j","0.67402874+1.10533101j","0.58989878+1.22907681j","0.48508091+1.36217361j","0.35384184+1.50466197j","0.18922616+1.65530759j","-0.01507502+1.80977315j","-0.26916190+1.96378897j","-0.58355932+2.10921824j","-0.96973323+2.23387960j","-1.44376810+2.32084864j","-2.01776923+2.34419079j","-2.70450605+2.26835910j","-3.51523154+2.04329073j","-4.44981648+1.60085003j","-5.49150900+0.85049732j","-6.59543668-0.32686610j","-7.66333698-2.07602291j","-8.52012914-4.57319447j","-8.86225145-7.99884597j","-8.20342140-12.49729771j","-5.79572502-18.10718010j","-0.56354036-24.56039977j","8.95222771-31.02722158j","24.50675767-35.60779374j"]
[{"$nulls":15},"Bessel, first kind, first order (k'√(-j))",{"$f":"zbesselj(1,Q18)","v":"0.18439461-0.17297355j"},{"$f":"zbesselj(1,R18)","v":"0.19585366-0.18231651j"},"0.20896452-0.19273475j","0.22149433-0.20241399j","0.23615443-0.21338763j","0.25146582-0.22443758j","0.26858851-0.23629037j","0.28620451-0.24792385j","0.30541850-0.25996106j","0.32718559-0.27277627j","0.34924295-0.28487621j","0.37463307-0.29771035j","0.40118947-0.30989872j","0.43078110-0.32202031j","0.46233839-0.33329052j","0.49759817-0.34391539j","0.53552961-0.35309714j","0.57691688-0.36054488j","0.62332236-0.36581625j","0.67373378-0.36798306j","0.72962350-0.36619931j","0.79075965-0.35935999j","0.85843011-0.34597843j","0.93223768-0.32452259j","1.01316852-0.29277321j","1.10120444-0.24828648j","1.19739605-0.18728738j","1.30018138-0.10664008j","1.40937738-0.00115457j","1.52365604+0.13551250j","1.63910334+0.30921613j","1.75150869+0.52902084j","1.85323388+0.80437508j","1.93290739+1.14546214j","1.97443467+1.56640873j","1.95373520+2.07757590j","1.83761264+2.68951093j","1.57926680+3.41079945j","1.11537629+4.23891946j","0.36200249+5.15504780j","-0.79094227+6.11297898j","-2.47628693+7.01554315j","-4.85451764+7.69182835j","-8.08666715+7.84921192j","-12.29460261+7.02249479j","-17.49248613+4.49995180j","-23.39366599-0.73451353j","-29.16440515-10.04961194j","-32.93843570-25.07101345j"]
[{"$nulls":14},"Eq 6.36","Impedance of microperforated layer (z1)",{"$f":"IMDIV(Q17,IMSUB(1,IMDIV(IMPRODUCT(2,Q20),IMPRODUCT(Q18,Q19))))","v":"3.10817684808118+0.132400071519291j"},{"$f":"IMDIV(R17,IMSUB(1,IMDIV(IMPRODUCT(2,R20),IMPRODUCT(R18,R19))))","v":"3.10822150858254+0.148285760999249j"},"3.10828216445948+0.167350566442197j","3.10834900060958+0.186415028662679j","3.10844258767614+0.209715555523304j","3.10855589742121+0.235134186951648j","3.10870532921746+0.264787287316007j","3.10888408602556+0.29655765160247j","3.10911143212325+0.33256438875582j","3.10941256192499+0.374922414702611j","3.10976736497119+0.419394435157537j","3.11024149400585+0.472333792602272j","3.11081639919539+0.529502654659072j","3.11155693018135+0.595132836377986j","3.11246808076372+0.667102902801318j","3.11364018807542+0.749639917653225j","3.11508886508838+0.84061955775192j","3.11689926903115+0.942146420966211j","3.11922333376265+1.05843321717397j","3.12211053773236+1.18734163623126j","3.12576551708779+1.33306499909574j","3.13032737460103+1.49555649742144j","3.13608712606924+1.67897081737831j","3.14325365611369+1.88321697881115j","3.15222556644192+2.11238173073809j","3.16339123183996+2.36839408642213j","3.17740682544372+2.65730369129166j","3.19471467036012+2.97877886866228j","3.21615045090539+3.33864128025168j","3.24268074020904+3.74251814077177j","3.27507702483894+4.19168286113286j","3.31459098668212+4.69334436949696j","3.36236827273678+5.25230743485549j","3.41949951670446+5.87302112382588j","3.48752454564221+6.56553727856276j","3.5671924733775+7.33343846057768j","3.65928251708889+8.18394109450731j","3.76456008565906+9.12780254445401j","3.88306609459779+10.1735896888405j","4.01452967083104+11.331752311891j","4.15864841838063+12.6165622612676j","4.3145916139671+14.040597185376j","4.4821806910581+15.6239491956589j","4.66101282423762+17.3849199461735j","4.85097844516522+19.3435882233855j","5.05290201434801+21.5286825731542j","5.26708840235931+23.9631983817741j","5.49466606297427+26.6802477379534j","5.73660651769572+29.7141610822304j"]
[]
[{"$nulls":15},"Intermediate values for Eq 6.39"]
[{"$nulls":15},"kd",{"$f":"Q13*micro_cavity_depth","v":0.07433542776482656},{"$f":"R13*micro_cavity_depth","v":0.08325567909660574},0.09395998069474076,0.10466428229287579,0.11774731757948526,0.13201971971033197,0.14867085552965312,0.16651135819321147,0.1867305945452443,0.21051793142998879,0.2354946351589705,0.26522880626490114,0.29734171105930624,0.33421208323066015,0.37465055593472585,0.42103586285997757,0.4721786371621782,0.5292682456855651,0.5946834221186125,0.6672347996170831,0.7493011118694517,0.8408823588757179,0.9443572743243565,1.0597258582153672,1.189366844237225,1.3344695992341662,1.4986022237389034,1.6817647177514359,1.8875251818044758,2.1194517164307345,2.37873368847445,2.6701285653125697,2.997204447477807,3.3635294355028718,3.7762397304531885,4.238903432861469,4.7574673769489,5.340257130625139,5.994408894955614,6.72824823784998,7.552479460906377,8.476617498878701,9.5149347538978,10.680514261250279,11.987628423066989,13.45649647569996,15.103769554968517,16.953234997757402,19.0298695077956]
[{"$nulls":15},"At top of air layer (zair) = jrc * cot(kd)",{"$f":"IMPRODUCT(\"-j\",airImpedance,COS(Q24)/SIN(Q24))","v":"-5552.0037028544j"},"-4954.81710108971j","-4387.55879095772j","-3936.02775127461j","-3495.27972350676j","-3113.68235810481j","-2760.60565733285j","-2460.15670756504j","-2188.47656146595j","-1934.9717385615j","-1723.18410044568j","-1522.19980137281j","-1349.33870802331j","-1190.74665915136j","-1051.49593840777j","-923.309654756157j","-809.603599076598j","-706.869667226076j","-611.320006576913j","-524.868952178677j","-444.454524788727j","-369.959672888879j","-299.219602622167j","-231.860851510529j","-165.83188429664j","-99.5752971135256j","-29.9022395760043j","46.0716345286939j","135.520942387683j","252.737790827357j","432.544199815746j","811.033786627409j",{"$f":"IMPRODUCT(\"-j\",airImpedance,COS(AW24)/SIN(AW24))","v":"2843.68849496212j"},"-1832.32979969628j","-561.587496511421j","-211.846162737658j","18.6513095744757j","300.120881419832j","1391.78479238492j","-866.85412409751j","-128.582869002319j","296.830120889274j","-4573.71588877782j","-134.75721748608j","632.828312732427j","-334.817937115874j","598.965346235476j","-139.560184000319j","-2268.16860541369j"]
[{"$nulls":15},"2√(rwh) / 2e",{"$f":"SQRT(2*Q12*airDensity*airViscosity)/(2*micro_porosity)","v":13.15726237418807},{"$f":"SQRT(2*R12*airDensity*airViscosity)/(2*micro_porosity)","v":13.924337670611559},14.792414651556944,15.61229909020388,16.559343834893596,17.534242796693782,18.607178893277997,19.691987180841455,20.853326967087565,22.141761054958874,23.418448635305822,24.852950685134896,26.31452474837614,27.8983607961432,29.53798077126218,31.313178778747247,33.160477828581506,35.1079549199973,37.21435778655599,39.41912294017497,41.77301301183467,44.25223738534179,46.895997479952285,49.67803150468079,52.62904949675228,55.74705827884783,59.07596154252436,62.58211427570408,66.3000704556824,70.25534590591747,74.42871557311199,78.85581037781202,83.54602602366934,88.50447477068359,93.77722805515118,99.35606300936158,105.25809899350456,111.51895650822281,118.15192308504872,125.17529279262769,132.6210277573495,140.50083521669728,148.85743114622397,157.71162075562404,167.0837635455331,177.02459674135721,187.54707193123653,198.69818668820068,210.51619798700912]
[{"$nulls":15},"1.7j rwa / e",{"$f":"IMPRODUCT(\"j\",1.7*Q12*airDensity*micro_hole_radius/micro_porosity)","v":"15.9921963893504j"},"17.9112599560724j","20.2141362361389j","22.5170125162053j","25.331639080731j","28.4021407874862j","31.9843927787007j","35.8225199121448j","40.1723973300481j","45.2899001746402j","50.663278161462j","57.0601567172021j","63.9687855574015j","71.9009149665192j","80.6006698023258j","90.5798003492805j","101.582431465154j","113.864438292175j","127.937571114803j","143.545954790809j","161.201339604652j","180.903725556331j","203.164862930307j","227.984751726579j","255.875142229606j","287.091909581618j","322.402679209303j","361.807451112663j","406.073850718384j","455.969503453158j","511.750284459212j","574.439694305465j",{"$f":"IMPRODUCT(\"j\",1.7*AW12*airDensity*micro_hole_radius/micro_porosity)","v":"644.805358418607j"},"723.614902225325j","812.403576578998j","911.939006906315j","1023.50056891842j","1148.87938861093j","1289.61071683721j","1447.48567959288j","1624.807153158j","1823.6221386704j","2047.00113783685j","2297.75877722186j","2578.9655585322j","2894.97135918576j","3249.35843117376j","3647.2442773408j","4094.00227567369j"]
[{"$nulls":14},"Eq 6.39","Overall impedance (zh)",{"$f":"IMPRODUCT(IMSUM(IMDIV(Q21,micro_porosity),Q25,Q26,Q27),$U$4)","v":"593.424722285643-5177.39750975652j"},"594.153886379211-4611.45257234571j","594.980951280408-4072.67604104328j","595.763885382001-3642.64763596939j","596.671312059181-3221.47914470994j","597.608600212658-2855.25767942784j","598.644766007875-2514.56436763663j","599.697570204284-2222.68870730535j","600.831374054077-1956.5740189565j","602.098401042724-1705.62986830107j","603.364423918297-1493.25140174781j","604.801051391434-1288.48004324781j","606.28195792548-1108.86427709711j","607.90871620892-940.113441737166j","609.61979087245-787.630962250426j","611.507052004982-642.367984979183j","613.513769528608-508.171880914529j","615.682246987645-381.112220539913j","618.096092606865-256.361149857522j","620.707645117045-136.357747699408j","623.602861678124-16.9598826105753j","626.785391117513+101.933687228171j","630.346474931757+223.614792170002j","634.30048523464+348.417363782063j","638.750796979261+479.514103574731j","643.768142268229+618.969557586414j","649.516445958552+771.632553393372j","656.046782575058+940.15148424894j","663.547849997677+1133.07795275976j","672.224322147786+1365.61546295316j","682.202359640822+1670.96451297455j","693.749441395516+2179.32072625847j",{"$f":"IMPRODUCT(IMSUM(IMDIV(AW21,micro_porosity),AW25,AW26,AW27),$U$4)","v":"707.088570502418+4260.00930883266j"},"722.428440421041+56.0860530052144j","740.100208505879+1463.09034097453j","760.236191552729+2028.82838383469j","782.998147960216+2509.25672055231j","808.562640107727+3068.02018668404j","836.949803177677+4421.59852506059j","868.126189358873+2664.03990172856j","902.06530153522+3764.60559378072j","938.622840594459+4617.4055164165j","977.805564141261+546.498146722374j","1019.55771611491+5282.59623156715j","1063.87794483512+6634.30364500674j","1110.96805721548+6430.45636855009j","1160.89721807364+8096.06331168045j","1213.92055049664+8283.90797041814j","1270.25562624987+7270.66322043235j"]
[]
[{"$nulls":15},"Reflection/Absorption coefficients"]
[{"$nulls":14},"Eq 1.22","Reflection factor",{"$f":"IMDIV(IMSUB(Q28,airImpedance),IMSUM(Q28,airImpedance))","v":"0.970069382482648-0.153901223886971j"},"0.962602276284871-0.171152565021349j","0.952627183561243-0.191316859483527j","0.941586259806643-0.210833348590272j","0.926714348053486-0.23371742922331j","0.908868860626338-0.257351168563348j","0.886087133794824-0.283011922454587j","0.859585118795941-0.3080416609815j","0.827306085014204-0.333123492966412j","0.786877588551167-0.357934609991273j","0.742361936156778-0.378348205201636j","0.687787629119753-0.395060281067022j","0.628425441211577-0.404044109045607j","0.561696133628152-0.403429568353803j","0.492501412355294-0.390699480862957j","0.42072841326483-0.363037043373262j","0.35316053456732-0.320068202316093j","0.293382576623488-0.261671583881105j","0.244991125526696-0.187631687395355j","0.214049518877755-0.103628410203993j","0.202831489238303-0.0130365504091718j","0.212618075816126+0.0771546638645499j","0.242532591003872+0.162270405215035j","0.289341969812659+0.236316088159109j","0.349244097535251+0.296559346139644j","0.417488996525446+0.341035509213711j","0.490522499989865+0.369833995289698j","0.563836401890311+0.383405784566225j","0.635558383239218+0.383410384517966j","0.705020809612828+0.371031912507827j","0.773065966082714+0.34608692272981j","0.846769312969943+0.301600627410468j",{"$f":"IMDIV(IMSUB(AW28,airImpedance),IMSUM(AW28,airImpedance))","v":"0.952243152558386+0.181556036609984j"},"0.273762596868754+0.0358585774713731j","0.725197012304282+0.348536002274003j","0.823327472228507+0.305389456414936j","0.871968609937569+0.268509423416446j","0.907340479022656+0.232629395827081j","0.951026528491164+0.173174327073951j","0.878734614549357+0.252072544229767j","0.931592506250402+0.195758150277863j","0.951698656854807+0.164949092394758j","0.485072446038422+0.202265078883235j","0.960445236171674+0.14581120041326j","0.973554576291493+0.118757861018605j","0.971135953137717+0.121755486751518j","0.98086116603345+0.0984198414600725j","0.981117788531546+0.0961159987927101j","0.975001558773713+0.10794810132335j"]
[{"$nulls":14},"Eq 1.25","Absorption coefficient (a)",{"$f":"1-POWER(IMABS(Q31),2)","v":{"v":0.03527980645582662,"d":"0.04"}},{"v":0.04410365717779774,"d":"0.04"},{"v":0.05589930841753454,"d":"0.06"},{"v":0.0689646144655498,"d":"0.07"},{"v":0.08657668038904964,"d":"0.09"},{"v":0.1077277702228614,"d":"0.11"},{"v":0.1347538430718327,"d":"0.13"},{"v":0.1662237586443268,"d":"0.17"},{"v":0.20459338013232775,"d":"0.20"},{"v":0.2527064756062958,"d":"0.25"},{"v":0.3057513913662606,"d":"0.31"},{"v":0.3708755515530745,"d":"0.37"},{"v":0.44182982278357663,"d":"0.44"},{"v":0.5217420368450494,"d":"0.52"},{"v":0.6047962744814565,"d":"0.60"},{"v":0.6911917074104587,"d":"0.69"},{"v":0.7728339826902694,"d":"0.77"},{"v":0.8454546459229171,"d":"0.85"},{"v":0.9047736982983345,"d":"0.90"},{"v":0.9434439560667945,"d":"0.94"},{"v":0.9586894353268013,"d":"0.96"},{"v":0.9488407116801965,"d":"0.95"},{"v":0.9148462578922969,"d":"0.91"},{"v":0.8604359309821066,"d":"0.86"},{"v":0.7900811145540149,"d":"0.79"},{"v":0.709397719235521,"d":"0.71"},{"v":0.6226104929317525,"d":"0.62"},{"v":0.5350885162645451,"d":"0.54"},{"v":0.44906201853813676,"d":"0.45"},{"v":0.36528097791365655,"d":"0.37"},{"v":0.28259285400001044,"d":"0.28"},{"v":0.19201879215802287,"d":"0.19"},{"$f":"1-POWER(IMABS(AW31),2)","v":{"v":0.060270383976140485,"d":"0.06"}},{"v":0.9237682029774057,"d":"0.92"},{"v":0.35261194846379906,"d":"0.35"},{"v":0.22886915338440705,"d":"0.23"},{"v":0.1675734328201114,"d":"0.17"},{"v":0.1226168193240641,"d":"0.12"},{"v":0.06555919454852954,"d":"0.07"},{"v":0.16428490963832532,"d":"0.16"},{"v":0.0938141488978842,"d":"0.09"},{"v":0.06706146345890163,"d":"0.07"},{"v":0.7237935599586609,"d":"0.72"},{"v":0.05628404214918148,"d":"0.06"},{"v":0.038088057428177,"d":"0.04"},{"v":0.04207056196919878,"d":"0.04"},{"v":0.028224907774474728,"d":"0.03"},{"v":0.02816959980304834,"d":"0.03"},{"v":0.037719167809513454,"d":"0.04"}]

{"sheet":"Flow Resistivity","index":4,"n_rows":95,"n_cols":10,"rows_kept":95}
[]
[null,"Flow Resistivity of Porous Absorbers"]
[null,"When calculating the absorption properties of porous materials such as fibreglass or Rockwool, the flow resistivity is the most important parameter!"]
[null,"The semi-empirical methods for estimating flow resistivity of porous absorbers are detailed below.  Please observe their limitations!"]
[null,"Properties of porous absorber"]
[null,"Porosity (e)",{"v":0.99,"d":"99.00%"},null,"All equation numbers refer to Cox and D'Antonio's book (see Acknowledgements for details)"]
[null,"(Average) Fibre diameter",7.5,"mm"]
[]
[null,"Bies and Hansen","Suitable for mineral and glass fibres of random fibre orientation with a typical diameter range of 1-10mm"]
[null,"Flow resistivity",{"$f":"27.3*10^12*(1-AbsorberPorosity)^1.53*(airViscosity/FibreDiameter^2)","v":{"v":7820.091753019004,"d":"7,820"}},"rayls/m","Eq 5.3","Accurate between 2,000 and 200,000 rayls/m"]
[]
[null,"Mechel (attributed to Sullivan)","Suitable for mineral and glass fibres with a typical diameter range of 1-30mm"]
[null,"Layered fibre orientation"]
[null,"Flow resistivity parallel to fibres",{"$f":"10^12*(3.94*airViscosity*(1-AbsorberPorosity)^1.413*(1+27*(1-AbsorberPorosity)^3))/((FibreDiameter/2)^2*AbsorberPorosity)","v":{"v":7815.953122578317,"d":"7,816"}},"rayls/m","Eq 5.4"]
[null,"Flow resistivity perpendicular to fibres",{"$f":"10^12*(G15*airViscosity*(1-AbsorberPorosity)^I15)/((FibreDiameter/2)^2*AbsorberPorosity^3)","v":{"v":12412.736247143097,"d":"12,413"}},"rayls/m","Eq 5.5","Factor =",{"$f":"IF(FibreDiameter<15,10.56,6.8)","v":10.56},"Exponent =",{"$f":"IF(FibreDiameter<15,1.531,1.296)","v":1.531}]
[]
[null,"Random fibre orientation"]
[null,"Flow resistivity",{"$f":"(10^12*4*airViscosity/(FibreDiameter/2)^2)*(((0.55*(1-AbsorberPorosity)^1.333)/AbsorberPorosity)+((SQRT(2)*(1-AbsorberPorosity)^2)/AbsorberPorosity^3))","v":{"v":7075.042935362363,"d":"7,075"}},"rayls/m","Eq 5.6"]
[]
[null,"Random fibre orientation and radius"]
[null,"Flow resistivity (Fibreglass)",{"$f":"10^12*(3.2*airViscosity*(1-AbsorberPorosity)^1.42)/(FibreDiameter/2)^2","v":{"v":6084.980226002421,"d":"6,085"}},"rayls/m","Eq 5.7"]
[null,"Flow resistivity (Mineral fibre)",{"$f":"10^12*(4.4*airViscosity*(1-AbsorberPorosity)^1.59)/(FibreDiameter/2)^2","v":{"v":3824.3873186004153,"d":"3,824"}},"rayls/m","Eq 5.7"]
[]
[null,"Explanation of Flow Resistivity"]
[null,"If a substance is not completely solid, but has air gaps within its structure, then it is said to be a porous",{"$nulls":6},"Material","Typical porosities"]
[null,"material.  Many substances are porous, even the ones we would consider \"solid\" such as stone or brick.",{"$nulls":6},"Mineral Wool","0.92 - 0.99"]
[null,"The degree of openess within a substance's structure is known as its porosity, and this is measured as",{"$nulls":6},"Open cell acoustic foam","0.95 - 0.995"]
[null,"a value between zero and one, or simply as a percentage.",{"$nulls":6},"Felts","0.83 - 0.95"]
[null,"If the air gaps within the substance are sufficiently large, then they will form an interconnected labyrinth",{"$nulls":6},"Wood fibre board","0.65 - 0.80"]
[null,"of channels, and air will be able to pass directly through the structure.  However, these tiny channels will",{"$nulls":6},"Wood wool board","0.50 - 0.65"]
[null,"offer resistance to the flow of air.  Therefore, before air can flow through the substance, pressure must be",{"$nulls":6},"Porous render","0.60 - 0.65"]
[null,"exerted to force the air through against this resistance.  A sound wave hitting the porous material will",{"$nulls":6},"Pumice concrete","0.25 - 0.50"]
[null,"exert a pressure, and the porous material will then resist the flow of air through itself, and in doing so, use",{"$nulls":6},"Gravel and stone chip fill","0.25 - 0.45"]
[null,"up some of the sound energy. This is how fibreglass or Rockwool are able to absorb sound.",{"$nulls":6},"Ceramic filters","0.33 - 0.42"]
[{"$nulls":8},"Brick","0.25 - 0.30"]
[null,"The speed at which air flows through a sample of the substance, compared to the pressure difference",{"$nulls":6},"Sinter metal","0.10 - 0.25"]
[null,"exerted upon it is known as the flow resistance.  In mathematical language,",{"$nulls":6},"Firebrick","0.15 - 0.35"]
[null,"the flow resistance is represented by the Greek letter sigma (s), and is",{"$nulls":6},"Sandstone","0.02 - 0.06"]
[null,"the ratio of the pressure difference (from the surrounding pressure) DP,",{"$nulls":5},"Eq 5.2","Marble","~0.005"]
[null,"to the flow velocity U.  The units of flow resistance are Nm-3s or \"rayls\".",{"$nulls":6},"Table 5.1"]
[]
[null,"This value can be measured by taking a sample of the substance of a known thickness d, and subjecting it to a steady flow of air.  As long as the flow velocity"]
[null,"is small (in the order of a few millimetres per second), the pressure difference can be measured and the flow resistance calculated.  This gives a specific value"]
[null,"for that thickness of material.  Then, to find the flow resistance per unit"]
[null,"thickness (or the flow resistivity), we must divide by the thickness of the",{"$nulls":5},"Eq 5.1"]
[null,"sample.  The units of flow resistivity are Nm-4s or rayls m-1."]
[]
[null,"The work of Delany and Bazley"]
[null,"In the early 1970's, Delany and Bazley (D&B) conducted a large number of measurements to find the flow resisitivity of many porous absobers. Then through a"]
[null,"process of curve fitting, they were able to derive a set of formulae to make a direct estimate of the charactaristic impedance and wavenumber of the material."]
[null,"These equations have been proven to give reliable estimates, and are widely used in prediction models."]
[]
[null,"What is a wavenumber?"]
[null,"The wavenumber is a frequently used value that describes how a wave travels through a medium.  It is the angular reciprocal of the"]
[null,"wavelength.  The wave number represents \"radians per metre\".  In otherwords, what angle of rotation (in radians) does this wave make"]
[null,"in the space of one metre?  If we are talking about a sound wave travelling through air, then the wavenumber is calculated using the"]
[null,"formula on the right; where k represents the wavenumber and l is the wavelength."]
[]
[null,"For sound travelling through air, the value of the wavenumber is real.  That means, it is represented by a number you can count to.  However, the wavenumber"]
[null,"for sound travelling through a porous absorber is complex.  This means it is a number containing two parts, a real part and an imaginary part (some multiple"]
[null,"of the square root of -1).  The imaginary part is represented by the letter j (in physics at least - in maths, you'll see it represented by the letter i)."]
[]
[null,"What is impedance?"]
[null,"Impedance is a measure of the resistance offered by a material to the average pressure created by a sound wave of a particular freqency.  This is very similar"]
[null,"to the concept of flow resistivity, but with the following difference.  Flow resistivity relates to a steady flow of air through a porous material when subjected to a"]
[null,"constant pressure gradient.  Impedance, on the other hand, relates to the resistance offered by a porous absorber to an oscillating pressure gradient.  E.G. a"]
[null,"sound wave.  For sound travelling through air, the flow resistivity and impedance are the same, but for sound in a porous absorber, the values are different."]
[null,"The impedance of a porous absorber is a complex value, whereas the impedance of air is purely real."]
[]
[null,"When D&B came to derive their formulae for the impedance and wavenumber of a porous absorber, they used the impedance and wavenumber of air as their"]
[null,"starting point, and then derived values that could be used as a scale factors and so arrive at the impedance and wavenumber of the porous absorber."]
[]
[null,"The impedance of a material is represented by the letter z.  The impedance of air (zair) is given by:"]
[null,"Where r0 is the density of air and c is the velocity of sound (both at 1 atmosphere and 20°C)"]
[]
[null,"D&B derived the following equations that scale the impedance and wavenumber of air to derive the corresponding values for a porous absorber."]
{"$rows_empty":8}
[null,"Where X is the dimensionless quantity:",null,null,"and f is the frequency of sound and s (sigma) is the flow resistivity."]
[]
[null,"The values produced by these equations are complex numbers.  The real part is known as the resistance and relates to energy loss, and the imaginary part"]
[null,"is known as the reactance and relates to extra \"virtual\" mass the absorber appears to have due to the resistance created by the viscous air/fibre boundary layers."]
[]
[null,"Range of accuracy for values derived using Delany & Bazley's formulae"]
[null,"D&B's formulae are accurate within the following boundaries:"]
[]
[null,"● The flow resistivity values used to derive the dimensionless term X, must fall within the range: 1,000 < s < 50,000 rayls m-1"]
[null,"● The dimensionless term X must be within the range: 0.01 < X < 1.0"]
[null,"● The porosity of the material, e, must be close to 1.  Most porous absorbers achieve this."]

{"sheet":"Configuration","index":5,"n_rows":66,"n_cols":11,"rows_kept":66}
[]
[null,"Configuration settings"]
[]
[null,"Air variables",{"$nulls":5},"Air Constants"]
[null,"Air temperature",{"v":20,"d":"20.0"},"°C",{"$nulls":3},"Kinemetric viscosity",{"$f":"1.85*10^-5","v":{"v":1.8500000000000002E-5,"d":"0.000019"}},"m2s-1"]
[null,"Atmospheric pressure",{"v":1,"d":"1.000"},"Bar",{"$nulls":3},"Gas constant",287.05,"J Kg-1 °K-1"]
[null,"Density of air (r0)",{"$f":"(airPressureBar*oneAtm)/(gasConstant*(273.15+airTemp))","v":{"v":1.2041183163746156,"d":"1.204"}},"kg m-3","Effects of humidity are neglected",null,null,"Thermal conductivity",0.0241,"W m K-1"]
[null,"Sound velocity (c)",{"$f":"SQRT((gamma*oneAtm)/airDensity0)*SQRT(1+(airTemp/273.15))","v":{"v":343.3818984827985,"d":"343.38"}},"m s-1","Kinsler & Frey, Eqn 5.20",null,null,"Specific heat capacity",1.01,"J Kg-1 K-1"]
[null,"Impedance of air (z0)",{"$f":"sound_velocity*airDensity","v":{"v":413.4724334746265,"d":"413.47"}},"kg m-2s-1",{"$nulls":3},"Density at 0°C (r0)",1.293,"Kg m-3","Kinsler & Frey, Appendix A10, Table (c)"]
[null,"Intermediate term 2p/c",{"$f":"2*PI()/sound_velocity","v":{"v":0.018297951449803458,"d":"0.01830"}},"s m-1",{"$nulls":3},"Specific heat ratio",1.402,null,"Kinsler & Frey, Appendix A10, Table (c)"]
[null,"Intermediate term c/2p",{"$f":"sound_velocity/(2*PI())","v":{"v":54.65092651181678,"d":"54.65093"}},"m s-1",{"$nulls":3},"Pressure at 1 atmosphere",101325,"Pa"]
[null,"AirDensity/AirViscosity",{"$f":"airDensity/airViscosity","v":{"v":65087.476560790026,"d":"65087.477"}},"kg s m-5"]
[]
[null,"Spreadsheet configuration"]
[null,"Language for ATP function names","English"]
[]
[null,"Dimensions"]
[null,"Rigid backed porous absorber"]
[null,"Absorber thickness =","ta"]
[null,"Overall cavity depth =","d"]
[]
[]
[]
[]
[null,"Perforated Panel"]
[null,"Porous Absorber against Panel"]
[null,"Panel thickness =","tp"]
[null,"Absorber thickness =","ta"]
[null,"Repeat distance between holes =","D"]
[null,"Hole radius =","a"]
[null,"Overall cavity depth =","d"]
[]
[]
[]
[null,"Porous Absorber against Backing"]
[null,"Panel thickness =","tp"]
[null,"Absorber thickness =","ta"]
[null,"Repeat distance between holes =","D"]
[null,"Hole radius =","a"]
[null,"Overall cavity depth =","d"]
[]
[]
[null,"Slotted Panel"]
[null,"Porous Absorber against Panel"]
[null,"Panel thickness =","tp"]
[null,"Absorber thickness =","ta"]
[null,"Distance between slot =","D"]
[null,"Slot width =","w"]
[null,"Overall cavity depth =","d"]
[]
[]
[]
[null,"Porous Absorber against Backing"]
[null,"Panel thickness =","tp"]
[null,"Absorber thickness =","ta"]
[null,"Distance between slot =","D"]
[null,"Slot width =","w"]
[null,"Overall cavity depth =","d"]
[]
[]
[]
[null,"Microperforated Panel"]
[null,"Panel thickness =","tp"]
[null,"Distance between holes =","D"]
[null,"Hole radius =","a"]
[null,"Cavity depth =","d"]

{"sheet":"Acknowledgements","index":6,"n_rows":33,"n_cols":5,"rows_kept":33}
[]
[null,"Acknowledgements"]
[null,"My thanks go to the following reviewers who at various times, have suggested improvements, corrections and patiently endured the bug fixing cycle!"]
[]
[null,"Reviewers","Organisation","Contact"]
[null,"Angelo Campanella","Campanella Acoustics","http://www.campanellaacoustics.com"]
[null,"Jeff Szymanski","Auralex Acoustics","http://www.auralex.com"]
[null,"James Heddle","Independent consultant","http://directory.ourbrisbane.com/directory/listings/86305.html"]
[null,"Eric Desart","Independent consultant","http://www.acoustics-noise.com"]
[]
[null,"Source material"]
[null,"All equation numbers refer to Trevor Cox and Peter D'Antonio's book Acoustic Absorbers and Diffusors. Theory, Design and Application."]
[null,"The transfer matrix calculations in this spreadsheet are reimplementations of the MATLAB scripts printed in appendix B of the above book."]
[]
[null,"Configuration","Authors","Location","Source material"]
[null,"Air properties & sound velocity","Kinsler & Frey","Naval Postgraduate College","Fundamentals of Acoustics, Third Edition"]
[]
[null,"Porous Absorbers","Authors","Location","Source material"]
[null,"Rigid backed","Cox & D'Antonio","Salford University/RPG Diffusor Systems Inc","Chapter 5, Acoustic Absorbers and Diffusors. Theory, Design and Application"]
[]
[null,"Helmholtz Absorbers","Authors","Location","Source material"]
[null,"Perforated panels","As above","As above","Ibid, Chapter 6 and Appendix B.4"]
[null,"Slotted panels","As above","As above","Ibid, Chapter 6 and Appendix B.5"]
[]
[null,"Microperforated Panels","Authors","Location","Source material"]
[null,"Microperforated panels","As above","As above","Ibid, Chapter 6, section 5.2 and Appendix B.6"]
[null,"Implementation of Bessel function","Gordon Everstine","Gaithersburg, Maryland, USA","http://www.efg2.com/Lab/Mathematics/Complex/Bessel.htm"]
[null,"VBA functions for complex numbers","Leonardo Volpi et al","Foxes team, Italy","http://digilander.libero.it/foxes"]
[]
[null,"Calculations for microperforated panel absorbers"]
[null,"I am greatly indebted to Gordon Everstine for sending me his FORTRAN implementation of a Bessel function taking a complex parameter."]
[null,"After translating the FORTAN code into VBA, I used a combination of VBA functions supplied by the Analysis ToolPak and the Foxes Team in Italy to implement a"]
[null,"high perfomance version of the algorithm."]