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I. §16.] LONGITUDINAL VIBRATIONS. 33
also those in the bracket b. This is due to the fact that, in the case there represented, the vibrating particles move uniformly, i.e. with equal velocity, throughout their paths. If we take other modes of vibration, we shall find that this equidistance no longer exists. Fig. 15 shows three distinct modes of vibration with the wave resulting from each, on the plan of Fig. 14. The extent of vibration and length of wave are the same in the three cases.
In (I) the particles move quickest at the middle, and slowest at the ends of their paths; in (II) fastest at the ends and slowest in the middle; in (III) slowest at the left end, and fastest at the right.
The shortest distance separating any two particles contained in a is, in (I), that between 7 and 8; in (II), that between 8 and 9; in (III), that between 5 and 6. The corresponding greatest distances are, in (I), between 2 and 3 ; in (II), between 1 and 2 ; in (III), between 4 and 5. The remaining particles likewise exhibit differences of relative distance in the three cases. Thus, the positions of greatest shortening and greatest lengthening occupy different situations in the wave, and the intermediate variations between them proceed according to different laws, when the modes of particle-vibration are different. The more particles we lay down in