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

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VI. § 71.] COMPOSITION OF VIBRATIONS.              141
respective positions which a particle originally at O would at a given moment occupy if the forces acted separately.
71. In determining the corresponding position of this particle under the forces acting simultaneously we employ the following principle:—The resultant displacement is equal to the sum or difference of the component displacements, according as these are pro­duced in the same or in opposite directions.
In the application of this principle four different cases present themselves. In (l), crest falls on crest; in (2), trough on trough, and the displace­ment, Oc, of the particle from its position of rest, 0, is in both these instances equal to the sum of the displacements Oa and Ob. In (3) and (4), where the crest of one wave meets the trough of another, Oc is equal to the difference between Oa and Ob ; c being above or below the undisturbed line, according
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E-Book - An Annotated Compendium of Old Time American Songs by James Alverson III