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The Theory Of Sound Which Constitutes The Physical Basis Of The Art Of Music.

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36                          ASSOCIATED WAVE.                  [I. § 18.
of particles in their positions of rest. Nevertheless, if the vibrations in the two cases are identical in all respects save direction alone, the distance which, at any moment, separates an assigned par­ticle from its position of rest will be the same whether the vibrations are longitudinal or transverse. It is therefore only necessary to construct the wave corresponding to any system of transverse vibrations, in the way shown in § 12, in order to obtain the means of fixing the position of an assigned particle at any given moment for the same system of vibra­tions executed longitudinally.
Let AB and CD, Fig. 16, be lines of particles executing vibrations transverse to AB and along CD respectively. Let a and b be corresponding particles in their positions of rest. Draw the transverse wave for any given instant of time : the particle originally at a will now be at a', and that originally at b will be at b', if bb' be made equal to aa'.
By performing the same process for different instants, we can find as many corresponding posi-
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E-Book - An Annotated Compendium of Old Time American Songs by James Alverson III