A transverse wave is described by equation y = {y_0},sin ,2π ,left[ {ft - frac{x}{λ }} right

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14.Waves and Sound

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A transverse wave is described by the equation $y = {y_0}\,\sin \,2\pi \,\left[ {ft - \frac{x}{\lambda }} \right]$ . The maximum particle velocity is equal to four times the wave velocity if

A

$\lambda \, = \,\frac{{\pi {y_0}}}{4}$

B

$\lambda \, = \,\frac{{\pi {y_0}}}{2}$

C

$\lambda \, = \,\pi {y_0}$

D

$\lambda \, = \,2\pi {y_0}$

Solution

Max particle velocity $\left(\frac{\partial y}{\partial t}\right)_{\max }=y_{0} f 2 \pi$

wave velocity $=f \lambda$

$4 f \lambda=y_{0} f 2 \pi$

$\lambda=\frac{\mathrm{y}_{0} \pi}{2}$

Standard 11

Physics

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