Mathematically, sound waves satisfy the wave equation.
Because the wave equation is linear with constant coefficients, sine waves
are eigenfunctions, and are thus enormously important. In music and acoustics,
sine waves are often called pure tones. Physically, if
the source is a steady-state sine wave with frequency f, then the response
at any other point in space is also a sine wave of frequency f; only the
amplitude and phase change as one moves around. This is not true of any
other function.*
For spatial sine waves, we specify the wavelength
, which is the distance for one cycle. For temporal sine waves, it is
common to specify the frequency f (in Hertz or cycles per
second), the angular frequeny
(in radians per
second), or the period T (in seconds). These quantities
are linked to the speed of sound c through the following
basic equations:
It is useful to remember that a 1-kHz tone has a period of 1 ms and a wavelength
of about 1 foot.
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