Generation of Sound

Webster's Ninth defines sound as "the sensation perceived by the sense of hearing". A more technical definition might be: sound consists of a local pressure disturbance in a continuous medium (such as the atmosphere) in the range of 20 to 20,000 Hz, which is the frequency range audible to humans. Frequencies below 20 Hz are infrasonic, and frequencies above 20,000 Hz are ultrasonic.

If the pressure disturbance raises the pressure in the medium above the average pressure, this is referred to as a condensation; if it lowers the pressure below the average, it is called a rarefaction. These condensations and rarefactions in the medium will move through it as the disturbed air particles collide with others, creating another disturbance in the medium further away from the source. This process is called sound propagation.

Propagation Velocity (Speed of Sound)
The speed of sound is approximately 343 meters per second in standard Earth atmosphere, but it can vary greatly depending on the properties of the medium the sound is traveling through. The following factors influence the speed at which sound propogates:

• Stiffness of the medium. Steel is much stiffer than water, which is in turn much stiffer than air. The stiffer (less elastic) the medium is, the faster sound will travel through it.

  Density of the medium; the more dense, the slower the sound waves will travel.

• Temperature. Sound travels faster through a hot medium than a cold one. As noted above, the speed of sound at room temperature (about 70 degrees F) is 343 m/s, but in the warmer vocal tract, at 98.6 degrees, it travels slightly faster, at 350 m/s.

Wave Interference
When two or more sound waves are brought into contact with one another, a new resulting wave is created. This new wave can then interfere with the continued motion of the previously-existing sound waves, and hence, is called interference. Mathematically, interference is the phase-matched sum of waveforms involved.

There are two basic forms of interference: constructive and destructive. The names describe what one would expect to happen—constructive interfence causes an increase in the amplitude of the waveform, while destructive interference causes a decrease. The extreme cases can be demonstrated with two identical waveforms. If the two waveforms, having equal amplitude and frequency, interfere, and their crests and troughs are in sync (i.e., in phase), the resulting waveform will have the same frequency with doubled amplitude. On the other hand, if the crests and troughs are out of sync (i.e., 180 degrees out of phase), the resulting waveform will have zero amplitude—in other words, a flat line.

"Interference" can have a negative connotation, as people associate the term with undesirable noise. However, interference is present in and responsible for almost everything we hear in a daily basis. The symphony orchestra is a good example; the combined orchestral sound perceived by the listener would not be possible without interference. It is the result of many sound waves being beautifully combined (via interference) in the air.

Standing Waves
To illustrate the behavior of waves, we will use the concrete example of a telephone cord attached to a wall-mounted telephone. You can sway the cord between the handset and the wall unit back and forth. This represents a standing wave with a half period, hence the wavelength is twice the distance between the two endpoints. (A node can be defined as an area of little motion. Note that this simple waveform has two nodes.) You should end up with a waveform that looks something like this:

Now, increase the swaying speed. You should be able to sway it fast enough that a complete waveform (having two nodes) is visible at once. Now the wavelength is equal to the distance between the two endpoints.

You can continue swaying faster and faster to create waveforms with increasing numbers of nodes. (Of course, your arm will eventually grow tired.)

This demonstrates a few fundamental concepts of standing waves. The first, and most important, is that standing waves always have a discrete number of waveforms, and only consist of whole or half wavelengths. This is due to the fixed zero crossings at the boundaries of the waveform. In addition, more energy is required to add an additional node to the standing wave given a particular set of boundaries. (Note how much harder your arm had to work to create three or four nodes rather than one in the phone cord demonstration.)