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T. § 15.] LONGITUDINAL VIBRATIONS. 31
and 7, one-eighth of the period of a complete vibration. Thus, proceeding from left to right along the line (0), we have the first particle beginning a forward swing, the second, third, fourth and fifth particles entering respectively on the fourth, third, second and first quarters of a backward swing, and the sixth, seventh, eighth and ninth particles on the fourth, third, second, and first quarters of a forward swing.
Since the ninth particle is just beginning a forward swing, its situation is exactly the same as that of the first. Beyond this point, therefore, we have only repetition of the state of things between the first and ninth particles. The row (0) is therefore made up of a series of groups, or cycles, of the same number of particles arranged in the same manner throughout. Two such cycles, included by the large brackets A and B, are shown in (0). Each cycle is divided by the sub-brackets a, a' and b, b' into two parts. In a and b the distances between successive particles are less than, and in a' and b' greater than, the corresponding distances when the particles occupied their undisturbed positions. The cycles correspond to complete waves on the surface of water, the shortened and elongated portions of each cycle answering to the crest and trough of which each water-wave consists.