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A transverse wave is represented by $y = A \sin (ωt - kx)$ . For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

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$\frac{πA}{2}$

$πA$

2 $πA$

answer is C.

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Detailed Solution

Wave velocity v = $\frac{λ}{T} = \frac{ωλ}{2 π}$

Maximum particle velocity ${(v_{\max})}_{ρ}$ = $Aω$

Given, $v = {(v_{\max})}_{ρ}$

$\frac{ωλ}{2 π} = Aω \Rightarrow λ = 2 πA$

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