A wave might be representable as a combination such as 1.4 cos x + 2.8 sin x - 1.103 cos 2x + 3.32 cos 3x + 5.6 sin 3x. Normally, a wave selected at random can only be represented by an infinite number of such terms; in other words, the combination doesn't stop, but goes on forever, though the numbers in front of the sines and cosines get smaller and smaller.
Musically, when an instrument plays a note, the basic note can be represented by A.cos Lt + B.sin Lt. The number L has to do with how high the note is (pitch), and A and B have to do with how loud it is; t is time.
Trigonometry is the mathematics of sound and music.
A microphone measures air pressure. Sound is just the variation of air pressure. Sound can be represented mathematically by a function f(t) giving the air pressure at time t . More precisely, f(t) represents the difference between the air pressure at time t and the average air pressure.
The simplest sounds, called pure tones are represented by functions of the form
f(t) = A sin(2 pi w t)
This family of functions has two parameters that we can hear -- w, the frequency, and A, the amplitude.
The b in both of the graph types
- y = a sin bx
- y = a cos bx
affects the period (or wavelength) of the graph. The period is the distance (or time) that it takes for the sine or cosine curve to begin repeating again.
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