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A transverse wave is represented by $y = A \sin (ω t - k x) .$ For what value of the wave length is the wave velocity equal to the maximum particle velocity?

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$2 π A$

$π A$

$\frac{π}{2}$

answer is D.

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Detailed Solution

$y = A \sin (ω t - k x) .$

Wave velocity is

$ν = \frac{ω}{k}$

$\Rightarrow \frac{dy}{dt} = Aω \cos (ωt - kx) .$

Maximum particle velocity is

$v_{y (\max)} = Aω$

According to question

$\frac{ω}{k} = Aω$

$\Rightarrow \frac{λ}{2 π} = A \Rightarrow λ = 2 πA$

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