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20 TTRANSVERSE VIBRATIONS. [I. § 9.
returned to their original positions and the wave A is where B was in (0). The particles have completed one vibrational cycle and the wave has advanced by its own length. This result may be thus generalised : While an individual particle performs one complete vibration the wave advances one wave-length. The proposition proved above (p. 15) for water-waves is, therefore, also true of waves due to transverse vibrations i.e. such as are executed perpendicularly to the direction of wave-propagation.
As waves thus produced are of leading importance in the theory of Sound, it is necessary to study them in some detail.
Let a particle originally at rest at 0 in the initial line (Fig. 7 bis) be cooperating in the transmission of a wave This wave is drawn in the figure in two positions such that the two points of its curve the most distant from the initial line, A and A\ are situated in two straight lines OA and OA' drawn through O in opposite directions each perpendicular to the initial line. It is evident that, at the moments when the wave is in these positions, the particle originally at O will be at A and A' respectively, and that these two points mark the limits of its vibration. Hence the line AA' is the extent of the particle's vibration. But by drawing parallels to the initial line through A and A' it will be seen, by reference