The Physics of Sound

Sound is vibration. The reason it is perhaps so hard to grasp that concept is because of the ways that the concept of sound has had to be represented graphically. How do you draw vibration? Would you see it like this?

Perhaps this would capture it for you more accurately.

Or we could try to explain it this way.

The problem with all of these representations (and others that you might have seen elsewhere) is that they all imply that there is some sort of linear movement of a wave through space. That a sound here moves to here and then to here . But it doesn't, not really.  So to understand how to record this illusive "thing" we call sound, it is useful, first, to understand something about its physics (or acoustical properties). Then we can talk about its psychoacoustics, or the ways that we actually hear, or experience, it. And that will take us into the realm of actually reproducing or recording it. First, its physics (from a layman's point of view).

We talk about sound "traveling" through the air, but this also gives the wrong impression. What actually happens is this. A string is plucked or bowed and it vibrates in the air. The string has mass and its vibration strikes against air molecules in its vicinity. Air molecules also have mass (although we don't ordinarily "experience" them unless we're in the midst of a windstorm or riding a bicycle quite fast). These molecules mutually support one another. To use an analogy. They are actually like millions of very tiny balls suspended in gelatin. Or as one book put it, imagine tennis balls connected together by springs. At any rate, each of them is supported by all those around it. So when we push on one of them, it pushes on those around it. So--to return to the vibrating string--the molecules that it strikes, in turn, strike others. One bangs into the next, and it into the next, and so on. Then, having struck, the first molecule returns to its original place where it is struck again, then returns, is struck again, etc. So each movement of the string causes the molecules it connects with to strike others and a chain reaction is set into motion. So it is not the first molecule struck which eventually strikes the mass of our eardrum, but actually the hundredth thousand or the millionth molecule in this chain that pushes against (and thus vibrates) our eardrum. Nothing by itself moves very far, but the cumulative banging around of molecule to molecule can carry the original vibration very great distances.

This brings us to three concepts that are crucial to understanding sound and that are based on this banging of molecule against molecule. These concepts are frequency, amplitude and attenuation.
Frequency refers to the pitch of sound. Sounds can be high-pitched, mid-pitched or low pitched. The higher the pitch of a sound the higher its frequency. Speakers reproduce high-pitched sounds with tweeters, while they reproduce low-pitched sound with woofers or sub-woofers. A high-pitched, or high frequency, sound has a very short wavelength. The length of a wave is its distance from one peak to the next, or one mid-point (or zero/zed point) to the next of the wave. Since all sound waves are "s"-shaped when represented on an oscilloscope, it is easy--with the proper instrumentation--to calculate their frequency. Here is a reproduction of a simple sound wave traveling through a telephone line. If you use the mid-point of a wave and trace a complete "s" from left to right, you will have traced one full cycle of the wave. The number of those cycles that occur per second is what is referred to as the waves frequency (also referred to as Hertz).  


This is actually what would be called a complex wave as opposed to a sine wave (or simple wave). A sine wave has a single frequency and its "s" is consistent across time. But a complex wave -- one that has been modulated or changed by the fundamental characteristics of sound (frequency, amplitude) -- has an "s" that varies as these characteristics vary. In this example the pitch of the loudness of the voice (amplitude) change as a person speaks, so the voltage changes, too.

You will also notice that each cycle has a plus side (above the line) and a minus side (below the line) and that these two sides mirror each other. If you could isolate one of these waves, cut it in half at the mid-point, and fold the bottom half toward the top half using the mid-point as an axis, you would create a full circle.

We begin with the basic "s" curve of a wave. This "s" represents one cycle, and if only one of these occurred each second, this would represent one Hertz.

When this "s" is bisected horizontally, and the bottom half folded left, it forms a circle. Since a circle is 360 degrees around, we thus know that each half of the "s" has 180 degrees (or half) the total. The half above the mid-point is its positive (+) phase and the half below the mid-point is its negative (-) phase.

One more note about phases before getting into compression and rarefaction. If you can imagine that, where the blue line above crosses the arc of the circle on the left is 0 degrees, then you can imagine that, when it crosses the circle on the opposite side, it is 180 degrees. Straight up (top of the circle) then becomes 90 degrees and straight down (bottom of the circle) is 270 degrees. In other words, no matter where we bisected this circle, the two points where the bisecting line crosses at opposite sides are 180 degrees apart, or 180 degrees out of phase. This will become important after we tackle compression and rarefaction. 
Now, remember the tiny balls (molecules) suspended in gelatin? Recapture that image.


What happens when a sound pressure wave strikes one of the balls suspended in this gelatin?

The molecule that is pressured pushes those around it. That molecule has been compressed. It, in turn compresses those it contacts, and so on. And when it springs back to its original position it rarefacts. It is the rapid cycling of compression and rarefaction that constitutes vibration. The more rapidly this compression/rarefaction occurs, the higher we say its frequency is. So a high frequency sound wave (at, say 18,000 Hz) causes this process to occur rapidly, while a low frequency sound wave (at, say 50 Hz) causes it to occur very slowly. The compression part of this cycle is its positive phase and the rarefaction portion its negative phase as represented on an oscilloscope.


If you're with me this far, we can now move into more detailed discussion of sound pressure level (SPL), or amplitude, the qualities of different frequencies, human apprehension of sound (or psychoacoustics), the richness of multiple frequency apprehension (or the role of harmonics) and the question of fidelity.

© Copyright Robert Fortner, 2003. All rights reserved. Last modified on January 12, 2004.