Sine Waves and the Geometry of Sound
Real-world waveforms aren’t perfect, regular up and down oscillations, nor
do they have just one frequency: sound almost always has energy at multiple
frequencies simultaneously. This fact is central in the construction of digital
audio devices such as equalizers and filters (Chapter 7). However, audio
engineers have found it extremely useful to have a basic waveform that can
be used as a sort of benchmark or building block to describe more complex
waveforms. This basic waveform, the sine wave, oscillates repeatedly at a
single frequency, and has no sound energy at any other frequency.
Meet the sine wave
The sine wave is a basic, periodic wave (one that repeats at regular intervals).
It sweeps up and down in a motion that’s a bit like the shape of the humps
and dips of a roller coaster (Figure 1.5). Sounds that we’d describe as “pure,”
like a ﬂute playing without vibrato, a person whistling, or a tuning fork, all
approximate the sine wave. It’s even the ideal wave shape for the electricity
in your home’s power outlets.
Figure 1.5 Computers are
capable of producing an
approximation of a pure sine
wave, as represented here in
the waveform display in
Apple Soundtrack Pro (top).
Shown in a graph of fre-
quency content over time
(bottom), this sine wave is a
single horizontal band; unlike
other sounds, the sine wave
carries energy at only a single
frequency.The haze around
the horizontal band is not due
to the presence of other fre-
quencies in the sine wave; it’s
caused by the limitations of
the analysis process.