Elements of natural philosophy (Volume 2-3) . In the first case Equation (24) gives tan A = {a + a) • sin^l - tan A(a + a), cos A = tan J.; When this valueis least; Least value; First case; whence JL, is equal to A\ and to A, and the maximum Conclusion;displacement will occur at the same place and at thesame time in the resultant wave, and in both compo-nent waves. In the second case, if we substitute in Equation (24)A = 180° + Af\ we find 66 NATURAL PHILOSOPHY. ; tan^ ^ (a-a).sin A =tan ^=tan(180o + A)=tanA\ (a—a) cos J. that is, A is equal to one at least of the arcs A andconclusi
Elements of natural philosophy (Volume 2-3) . In the first case Equation (24) gives tan A = {a + a) • sin^l - tan A(a + a), cos A = tan J.; When this valueis least; Least value; First case; whence JL, is equal to A\ and to A, and the maximum Conclusion;displacement will occur at the same place and at thesame time in the resultant wave, and in both compo-nent waves. In the second case, if we substitute in Equation (24)A = 180° + Af\ we find 66 NATURAL PHILOSOPHY. ; tan^ ^ (a-a).sin A =tan ^=tan(180o + A)=tanA\ (a—a) cos J. that is, A is equal to one at least of the arcs A andconclusion; A, and the greatest displacement in the resultant wavewill occur at the same place and time as in one of thecomponent waves. intensity of § 59. If the intensity of sound supposed somKi [n the component component waves be supposed equal atthe place of superposition,then will a = o!\ and Eq.(25) becomes ?waves; Fig. Consequence; ax 2a[_x cos A1 - A 2 (26) Reduction; Value ofarbitraryconstant; and Equation (24) reduces to , A sin A + sin A , Af + Atan A = -_ — — tan cos A + cos A 2 or, A = Af + A 2 When A - A = 0, then will Eq. (26) give (27). Supposition; a x 2af x , and A = A = A ; Illustration. that is, the intensity of soundin the resultant wave will bedouble that in either of theequal component waves; andthe greatest displacementwill occur at the same timeand place in the componentand resultant waves. Fig. 26.
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