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17 equidistant particles of the tube at rest; (0) gives the positions of the particles when they form parts of two complete waves A and B; and (1) to (8) show their positions at successive intervals of time, each equal toof the time that it takes a particle to perform one complete vibration. By a careful inspection of this diagram, it will bo seen that while each particle performs one complete vibration, the wave travels through a space equal to its own length. Taking the 1st particle in A, for example :—in (1), it has risen half way to its highest point; in (2), it has reached its highest point; in (3), it is descending again; it is passing downwards through its
original position; in (5), it is still sinking; in (6), it has reached its lowest position ; in (7), it is ascending again; in (8), it has reached its original position, having made one complete vibration. Now it is obvious from the figure, that during this time the wave A has passed through a space equal to its own length.
Let the curve in fig. 12 represent the outline section of the wave A in fig. 11. Through the deepest and highest points (d) and (c) of the protuberances, draw the dotted straight lines parallel to AB, the position of the tube when at rest. Through (d) draw (df) at right angles to AB; then as before (df) in the amplitude, of the wave. Now on comparing this with fig. 11 it will be seen that this amplitude is the same thing as extent of vibration of each particle.
Fig. 12.
If we suppose, that a particle takes a certain definite time, say one second, to perform its vibration, it is evident that the number of different modes in which it may get over its ground in this time is infinite. Thus it may move slowly at first, then quickly and again slowly; or it may start quickly, then slacken, again quicken, slacken again, and finish up quickly; and so on. In fig. 13, two waves of equal length and amplitude are represented after the manner of fig. 12. The extent and time of particle vibration being the same, they only differ in the mode of vibration. In (b) the particle at first moves more quickly than in (a); it then moves more slowly; and so on. Thus for example : supposing the time of a complete vibration to be one second, the particle in (a) reaches its highest position in one quarter, and its lowest, in three quarters of