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II LONGITUDINAL VIBRATIONS.. [I. § 16.
(1) shows the state of the row of particles when an interval of time equal to one-eighth of the period of a complete particle-vibration has elapsed from the moment shown in (0). The wave A has meantime advanced by one-eighth of its own wave-length into the position pointed to by the dotted lines.
The following rows (2), (3), (4), &c., show the state of things when two-eighths, three-eighths, four-eighths, &c, of a vibration-period has elapsed since (0). In each successive row the wave A is further advanced by one-eighth of its wave-length.
In (8), a whole vibration-period has elapsed since (0). Accordingly each particle has performed one complete vibration, and returned to the position which it held in (0). The wave A, meanwhile, has travelled constantly forward so as to be, in (8), where B was in (0), i.e. to have advanced by one whole wave-length. Hence, while any particle performs a complete vibration the wave advances by its own wave-length. Accordingly, for waves due to longitudinal vibrations, i.e. such as are executed in the line of wave-advance, a corresponding proposition holds good to that established in § 9 p. 20, for waves due to vibrations performed perpendicularly to the direction of wave-motion.
16. In the waves shown in Fig. 14, the particles in the bracket a are mutually equidistant, as are |
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