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A particle on the trough of a wave at any instant will come to the mean position after a time $(T=$ time period $)$
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Verified Answer
The correct answer is:
$\frac{T}{4}$
As total time period of a wave is $T$. The wave motion can be shown as

From figure, it can be seen that time taken by the particle to move from trough to its mean position i.e., from $R$ to $S$ is
$T^{\prime}=\frac{T / 2}{2}=\frac{T}{4}$

From figure, it can be seen that time taken by the particle to move from trough to its mean position i.e., from $R$ to $S$ is
$T^{\prime}=\frac{T / 2}{2}=\frac{T}{4}$
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