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Question

A wave travelling along positive x-axis is given by $$=A\sin { \left( \omega t-kx \right)  } $$. If it is reflected from a rigid boundary such that $$80$$% amplitude is reflected, then equation of reflected wave is


A
y=Asin(ωt+0.8kx)
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B
y=0.8Asin(ωt+kx)
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C
y=Asin(ωt+kx)
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D
y=0.8Asin(ωt+kx)
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Solution

The correct option is C $$y=-0.8A\sin { \left( \omega t+kx \right) } $$
On getting reflected from a rigid boundary the wave suffers an additional phase change of $$\pi$$.
Hence, if $$\quad { y }_{ incident }=A\sin { \left( \omega t-kx \right)  } $$
Then, $${ y }_{ reflected }=(0.8A)\sin { \left( \omega t-k(-x)+\pi  \right)  } =-0.8A\sin { \left( \omega t+kx \right)  } $$

Physics

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