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We may express a sound wave passing though a point in space as a function of time by recording the pressure at the point for each moment of time as illustrated by the following diagram. The vertical variable is excess pressure. The zero point is normal pressure (equilibrium), a positive value represents the amount of compression, and a negative value represents the amount of rarefaction. The horizontal variable is time, increasing to the right.
The resulting function h(t) is called a signal function (in the time domain.) Fourier theory states that all signal functions may be represented by an integral of sine waves. Periodic signal functions may be represented by a sum of sine waves in the form:
Where ω is a constant, called the fundamental angular frequency of the signal. The fundamental frequency f = ω/2π. Each term Aksin(kω t+φk) is called the kth harmonic or overtone of the signal h. Each Ak is the amplitude and each φk is the phase of the kth harmonic of the signal h.
A function h is periodic if there is a constant C such that h(t +C) = h(t) for all t. The period of a periodic function h is the smallest positive constant P such that h(t +P) = h(t) for all t. The (fundamental) frequency of a periodic function is 1/P where P is its period. The function sin(t) is periodic with period 2π. The phase of a wave is the amount that the original wave is shifted left (or right if phase is negative.) The period and phase of a periodic function is usually measured in radians or degrees. The frequency is the number of periods or cycles per second and is usually specified in Hertz, abbreviated as Hz. (1 Hz is 1 cycle per second.)
The signal displayed above is that of a sin wave. Most sound signals are more complex, consisting of the sum of many sin waves.
Sum of 4 sin waves: 
More: 
Another important quantity of sound wave is its intensity. The intensity of a sound wave is its average power divided by the area across which it is transported. The power is directly related to the square of its amplitude and the area is related to the square of the distance from the source. Thus, the sound intensity from a small round speaker decreases as 1/x2 where x is the distance from the speaker.
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