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Question

Equation of a plane progressive wave is given by y=0.5 sin 3π(tx3). On reflection from a denser medium its amplitude becomes 25 of the amplitude of the incident wave. The equation of the reflected wave is

A
0.2 sin (π(3t+x))
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B
0.2 sin (3πt+πx)
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C
0.5 sin (πt+x)
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D
0.2 sin(π(3tx))
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Solution

The correct option is B 0.2 sin (3πt+πx)
Given: yi=0.5 sin 3π(tx3)
We know, when waves propagate from rarere to denser medium there is phase change of π in reflected w.r.t. incident wave.
Also, direction of propagation of reflected wave will, be opposite to the incident wave
yr=Ar sin (3π(t+x3)+π)
Given Ar=25×0.5
yr=0.2 sin (3π(t+x3)+π)
=0.2 sin (3πt+πx+π)
=0.2 sin (π(3t+x))

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