Acoustics & Sound For Musicians - Online Book

The Theory Of Sound Which Constitutes The Physical Basis Of The Art Of Music.

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[I. § 10.
represented. One wave of (1) is as long as two of (2), and as three of (3). Therefore, in virtue of the fact proved in § 9, a particle makes one complete vibration in (1) while the long wave passes from A to B, two in (2) while the shorter waves there pre-
sented pass over the same distance, and three in the case of the shortest waves of (3). But the velocities of these waves being by our supposition equal, the times of describing the distance AB will be the same in (1), (2) and (3). Hence a particle in (2) vibrates twice as rapidly, and in (3) three times as rapidly, as in (1); or conversely, vibration in (1) is half as rapid as in (2), and one-third as rapid as in (3).
The roles of vibration in (1), (2) and (3), (by
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