Introduction to Acoustics
Here's a web version of a document I wrote several years ago to present an introduction to the basic principles of acoustics.
I wrote this document primarily because I realised that many people assume their natural sense of how–sound–ought–to–behave will somehow carry them intuitively to the right answer.
This is why so many people think that sticking egg boxes to the wall is an effective form of acoustic treatment...
Hmmmmm. Oh dear...
What is Acoustics?
Acoustics is the science of sound. Or, to put it in more technical terms, acoustics is concerned with "... the generation, transmission and reception of energy in the form of vibrational waves in matter." A huge number of scientific problems and disciplines fit into this definition, including:
- Noise and vibration control (E.G. reducing noise from traffic or machinery)
- Vibration and structural acoustics (E.G. generator rumble in a building)
- Musical acoustics (E.G. acoustics of musical instruments)
- Electroacoustics (E.G. loudspeaker and microphone design)
- Architectural acoustics (E.G. auditoriums, churches and listening rooms)
- Psychoacoustics (The human perception of sound)
- Underwater acoustics (E.G. sonar, echo ranging, military applications)
- Medical ultrasonics (E.G. medical imaging or using sound to kill cancer cells without surgery)
Fundamentals of sound
Sound can be defined either from a physical point of view, or a psychoacoustical point of view. Taking the physical point of view, sound can be defined as:
“Energy travelling through some elastic medium in the form of waves”
However, if we take the psycho-acoustical point of view, then sound is:
“The perception of sound created by the excitation our auditory system”
| Measured | Perceived |
|---|---|
| Frequency | Pitch |
| Harmonics | Partials |
| Intensity | Loudness |
| Early echoes | Spaciousness |
| Late echoes | Reverberation |
Table 1: Measured and perceived acoustic quantities
The definition that we take depends on the type of investigation being performed. If we are interested in how sound waves behave when they are contained within a room, then we are dealing with a problem in physics. If however, we want to understand how a listener in the room perceives the sound, then we are dealing with a problem in psychoacoustics. Often, there is a good deal of overlap between these two areas of investigation.
It is important to understand that there are differences between the physics of sound and the perception of sound. These differences become apparent when you compare the properties of sound that the physicist measures, and the properties of sound that we perceive. There is always a direct equivalence between the two.
The exact nature of these differences is covered in Chapter 3 (“The Ear and the Perception of Sound”) of F. Alton Everest’s book, The Master Handbook of Acoustics (Fourth Edition).
Range of Human Hearing
The human ear is a wonderfully constructed biological microphone. It is capable of detecting sounds as low in frequency as 20 cycles per second, and as high as 20,000 cycles per second.
“The delicate and sensitive nature of our hearing can be underscored dramatically by a little experiment. A bulky door of an anechoic chamber is slowly opened, revealing extremely thick walls, and three-foot wedges of glass fibre, points inward, lining all walls, ceiling, and what could be called the floor, except that you walk on an open steel grillwork.
“A chair is brought in, and you sit down. This experiment takes time, and as a result of your prior briefing, you lean back, patiently counting the glass fibre wedges to pass the time. It is very eerie in here. The sea of sound and noises of life and activity in which we are normally immersed and of which we are ordinarily scarcely conscious is now conspicuous by its absence.
“The silence presses down on you in the tomblike room; 10 minutes, then half an hour pass. New sounds are discovered, sounds that come from within your own body. First, the loud pounding of your own heart, still recovering from the novelty of the situation. An hour goes by. The blood coursing through the vessels becomes audible. At last, if your ears are keen, your patience is rewarded by a strange hissing sound between the “ker-bumps” of your heart and the slushing of blood. What is it? It is the sound of air molecules pounding against your eardrums. The eardrum motion resulting from that hissing sound is unbelievably small � only 1/100th of a millionth of a centimetre � or 1/10th the diameter of a hydrogen molecule!”
F. Alton Everest
This incredibly quiet background hiss is the absolute limit of the sensitivity of human hearing, and is taken as the reference point against which all other sound levels are measured.
In physical terms, this represents a sound pressure level of 20 micro Pascals, or expressed in terms of a power level, 1 x 10-12 Watts per square metre. (Remember this value, because it is used to define the lower limit of human hearing sensitivity)
At the opposite end of the scale, the ear can respond (albeit painfully) to sound pressure levels in excess of 20 Pascals or power levels of 1 Watt per square metre.
This means the ear is sensitive to sounds that vary in pressure level by a factor of 1 million, or in terms of power by a factor of 1,000 billion (1012)!
The ear’s huge range of sensitivity is called its dynamic range.
Sensitivity of Human Hearing
The sensitivity of the human ear changes with frequency and has been an area of extensive research in the telecoms, acoustic and medical fields. In 1933, Harvey Fletcher and Wilden Munson wrote a paper for the Journal of the Acoustic Society of America in which they described how the sensitivity of human hearing varies with frequency. Then in 1937, after many tests, they produced their first “Equal Loudness Curves”. Inspite of slightly different results produced by Robinson and Dadson in 1956, the Fletcher Munson Equal Loudness Curves are now taken as the standard response for the sensitivity of human hearing across the audibale range.
Figure 1: The Fletcher-Munson curve of perceived equal loudness
Each of the curved lines indicates an equal level of perceived volume.
As you can see, the sensitivity of the ear is far from even.
Look at the curve labeled 60 (under the heading Loudness level – phons). Notice that where 60 is printed on the line, you are perceiving the sound to be at the same level as the actual sound pressure level—60dB.
Now trace this line towards the level-hand vertical axis. The line you are following is the level your brain perceives as 60dB. Yet by the time we get down to 20Hz, the physical sound pressure level coming from a loud speaker is actually 104dB. Now trace this curve back towards the right, the actual sound level drops as the frequency rises.
By the time you get across to 4Khz, the sound level coming from the loud speaker has dropped to about 52dB—yet your brain still perceives this sound level to be 60dB.
This demonstrates that the sensitivity of the human ear varies with frequency. The ear is most sensitive to sound between roughly 2.5KHz to 5KHz—which is exactly the range of human speech (and also the range of a baby’s cry).
The purpose of this graph is to show the difference between the psycho-acoustic perception of loudness and the physical quantity measured by a sound level meter, as the frequency changes.
Since the ear’s sensitivity to sound is frequency dependent, a standard scale has been developed that describes “perceived loudness”. The units of this scale are known as Phons.
On early hi-fi amplifiers, there was a “loudness” control. This was an attempt to build a frequency dependent volume control that altered the volume according to the Phon scale, not the amplifier’s power scale.