Text: 17) When two simple tones, that is (as explained above), notes deprived of all the harmonic components which under ordinary circumstances accompany them, are sounded together very nearly in unison, there are heard what are called beats succeeding one another at regular intervals, their rapidity depending inversely on the smallness of the interval between the two tones. Their origin may be explained thus: Suppose the tones to be produced by vibrations numbering 500 and 501 per second respectively, then every 500th sound wave of the former will strike on the tympanum at exactly the same instant as every 501st of the latter and will reinforce it; while at the 250th of the first the corresponding wave of the other will be just half a period in front of it. Now a sound wave consists of a condensed and rarified stratum of air particles, and therefore the condensed portion of one wave here coincides with the rarified portion of the other and neutralises it. Thus there will be an alternate reinforcement and diminution of sound, every second, from the maximum intensity when both waves impinge on the tympanum at the same instant to the minimum when they counteract each other as much as possible and vice versa. In the above case it was supposed that the number of vibrations of one tone were only one more per second than those of the other; but if the difference of the numbers had been two, for instance, then in one second the first tone would have gained two vibrations on the other, and there would have been two beats; and in general the number of beats per second is always equal to the difference between the two rates of vibrations per second.

See Also: BEATS; DIFFERENCE TONES; LAW OF THE TRIANGLE; LAW OF SUPERPOSITION; LAW OF PROPORTION

Source: 125