Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013
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
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
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.
Properties of
Sine Waves
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