Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013

6

In order to have the proper terminology to discuss sound waves and the

corresponding sine functions, we need to take a little side trip into mathematics. We‟ll

first give the sine function as it applies to sound, and then we‟ll explain the related

terminology.

A single-frequency sound wave with frequency , maximum amplitude , and

phase is represented by the sine function

where x is time and y is the amplitude of the sound wave at moment x.

Equation 2.1

Single-frequency sound waves are sinusoidal waves. Although pure

single-frequency sound waves do not occur naturally, they can be created

artificially by computer means. Naturally occurring sound waves are

combinations of frequency components, as we‟ll discuss later in this chapter.

The graph of a sound wave is repeated Figure 2.4 with some of its parts

labeled. The amplitude of a wave is its y value at some moment in time given

by x. If we‟re talking about a pure sine wave, then the wave‟s amplitude, A, is

the highest y value of the wave. We call this highest value the crest of the

wave. The lowest value of the wave is called the trough. When we speak of the amplitude of

the sine wave related to sound, we‟re referring essentially to the change in air pressure caused by

the vibrations that created the sound. This air pressure, which changes over time, can be

measured in

Newtons/meter2

or, more customarily, in decibels (abbreviated dB), a logarithmic

unit explained in detail in Chapter 4. Amplitude is related to perceived loudness. The higher the

amplitude of a sound wave, the louder it seems to the human ear.

In order to define frequency, we must first define a cycle. A cycle of a sine wave is a

section of the wave from some starting position to the first moment at which it returns to that

same position after having gone through its maximum and minimum amplitudes. Usually, we

choose the starting position to be at some position where the wave crosses the x-axis, or zero

crossing, so the cycle would be from that position to the next zero crossing where the wave starts

to repeat, as shown in Figure 2.4.

Flash

Tutorial:

Properties of

Sine Waves