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April, 1935]
SOUND RECORDING
297
where PO represents the average atmospheric pressure upon which is superimposed a sinusoidal variation of amplitude P. Although a simple sine wave of this sort is rarely produced by any musical instrument, we may always analyze any musical note into a fundamental sine variation plus a number of harmonics or overtones.* Each of these, however, is itself a simple sine wave whose rate of variation is an integral multiple of the fundamental. The quality, or timbre, of a musical instrument depends upon the relative amplitudes of these harmonics.
If a perfect microphone and amplifier are used in recording, the current i in the last stage of the amplifier may be represented as
i = /o + / sin at (2)
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VALUES OF TIME,
FIG. 11. A simple sine wave.
There is a concept in sound recording which is very useful and which arises from this equation. Since the maximum value of sin otf is +1 and its minimum value — 1, the maximum value of * is /o + 1, the minimum value is /0 — 1 , and the average value is J0. The modulation, m, is defined as
* Consider the case of a musical instrument playing the A below middle C. The fundamental frequency of this note is a little more than 200 cycles per second, for simplicity, let us assume it to be exactly 200 cycles per second. In general, this note will consist of the fundamental 200-cycle variation, plus a harmonic with a frequency of 400 cycles per second, plus a third harmonic with a frequency three times the fundamental, or 600 cycles per second, and so on, the amplitude falling off rather rapidly in the higher harmonics.