Elements of natural philosophy (Volume 2-3) . the sum of the two arcs, we have Same; d = - - Sm f 2 * . 7,M + ... (22) Squaring Equations (a) and (b) and taking the sum, wefind, Transformations; a* = a2 + a* + 2 aa cos (^L - A) . . (23)and dividing Eqation (5), by Equation (a), we obtain deductions; tan J_ = .... (24). 0 . cos A + a . cos J. From Equation (22) we see that the length of the Conclusions; resulting wave is the same as that of the partial waves; but the value of A in that equation differing from A\ ELEMENTS OF ACOUSTICS. 65 ofmaximum and A, Equation (23), shows that the maximu
Elements of natural philosophy (Volume 2-3) . the sum of the two arcs, we have Same; d = - - Sm f 2 * . 7,M + ... (22) Squaring Equations (a) and (b) and taking the sum, wefind, Transformations; a* = a2 + a* + 2 aa cos (^L - A) . . (23)and dividing Eqation (5), by Equation (a), we obtain deductions; tan J_ = .... (24). 0 . cos A + a . cos J. From Equation (22) we see that the length of the Conclusions; resulting wave is the same as that of the partial waves; but the value of A in that equation differing from A\ ELEMENTS OF ACOUSTICS. 65 ofmaximum and A, Equation (23), shows that the maximum dis-Timeplacement for a given molecule does not take place ™^™ent nwith the same value of t, as for either of the compo-resultantwave;nent waves. The maximum displacement 0L which determines the x intensity of the sound, in the resultant wave, is given byEquation (23) to be * = I . /a* + a* +2aa. co${A - A!) X x \/ which depends upon the arcA — A. Its greatest va-lue is obtained by makingA! — A = 0, in which casewe have Fig. • \-5) General value ofthisdisplacement; When this valueis greatest; a af + ax x tt Greatest value; its least value results frommaking A! - A = 180°, inwhich case a x a - a x Fig. 24.
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