InterviewSolution
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InterviewSolution
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Two waves travelling in opposite directions produce a standing wave . The individual wave functions are given by `y_(1) = 4 sin ( 3x - 2 t)` and `y_(2) = 4 sin ( 3x + 2 t) cm` , where `x` and `y` are in cmA. The maximum displacement of the motion at `x = 2.3 cm is 4.63 cm`.B. The maximum displacement of the motion at `t = 2.3 s is 4.63 cm`.C. Nodes are formed at `x` values given by ` 0 , pi//3 , 2 pi//3 , 4 pi//3 , ….`D. Antinodes are formed at `x` values given by `pi//6 , pi//2 , 5 pi//6 , 7 pi//6,…` |
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Answer» Correct Answer - A::C::D `y = y_(1) + y_(2)` y = 4[ sin ( 3x - 2t) + sin( 3x + 2t)]` `y = 4[ 2 sin ( 3x) cos(2 t)]` `y = 8 sin ( 3 x) cos (2t)` `y = R cos ( 2t)` `R = Resultant Amplitude ` = 8 sin ( 3x)` `R = 8 sin [ 3 (2.3)]` `R = 8 sin (6.9)` `R = 4.63 cm` Nodes are formed at points of zero intensity , i.e., `I_(R) = R^(2) = 0` `sin^(2) ( 3x) = 0` `sin ( 3 x) = 0` `3x = 0 , pi , 2 pi , 3 pi , 4 pi ,...` `x = 0 , (pi)/(3) , ( 2pi)/(3) , pi , (4 pi)/(3) ,...` Antinodes are formed in between. |
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