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Q.

A transverse wave is represented by $y = 2 \sin (ωt - kx) cm$ . The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be ;

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a

$4 π$

b

$2 π$

c

$π$

d

2

answer is A.

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Detailed Solution

$y = 2 \sin (ωt - kx)$

Maximum particle velocity $= A ω$

Wave velocity $= \frac{ω}{k}$

$\begin{array}{l} \frac{ω}{k} = Aω \\ k = \frac{1}{A} = \frac{2 π}{λ} \\ λ = 2 πA \\ = 4 πcm \end{array}$

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A transverse wave is represented by y=2 sin (ωt−kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be ;