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106 RATE OF SEGMENTAL VIBRATION. [V. § 53.It is easy to confirm this by direct experiment, the swaying movement of the hand on the tube needing to be twice as rapid for a form of vibration with two segments as for a form with one, and so on.
53. Instead of comparing the different rates at which the same tube vibrates when divided into different numbers of ventral segments, we may compare the rates of vibration of tubes of different lengths divided into the same number of segments. Let us take as an example the two tubes
AB, CD, Fig. 36, each divided by three nodes into fourventral segments. By what has been already shown, the time of vibration of either tube will be that which a pulse occupies in traversing two of its ventral segments. Therefore the time of vibration of AB will be to that of CD as A2 is to C2, i.e. as one half of AB is to one half of CD, or as AB is to CD. This reasoning is equally applicable to any other case. Accordingly we have the general result that, when tubes of different lengths are divided into the same number of ventral segments, their times of vibration are proportional to the lengths of the tubes, or, which comes to the same thing, their rates |
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