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

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I. § 19.]              PENDULUM- VIBRATION.                      37
tions of the longitudinally-vibrating particle as we please. It is true that we learn nothing new by this, since we cannot construct the wave-curve without knowing beforehand the mode of the particle's vibra­tion [§ 12]. Still, when we are dealing with longitudinal particle-vibrations, and require to know the law of the variation of condensation and rarefac­tion at different points of a single wave, it is convenient to have a picture of the mode of vibration by which, as we know [§ 16], that law is determined. Such a picture we have in the form of the wave produced by the same mode of vibration when executed transversely. Let us call the wave so related to a given wave of condensation and rare­faction its associated wave.
19. Before leaving this portion of the subject, it will be advisable to draw the associated wave for that particular mode of longitudinal vibration in which each particle moves as if it were the extremity of a pendulum traversing a path which is very short compared to the pendulum's length. The meaning of this limitation will be easily seen from Fig. 17.
Let 0 be the fixed point of suspension ; OA the pendulum in its vertical position; AB a portion of a circle with centre 0 and radius OA ; a, b, c, d, points on this circle; AD a horizontal straight line through A ; aa', bb\ cc, dd' verticals through a, b,
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