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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
A transverse wave is described by the equation,
$y=y_{0} \sin 2 \pi\left(f t-\frac{\pi}{\lambda}\right)$
The maximum velocity of particle
$v_{\max }=y_{0} .2 \pi f \ldots .(1)$
The velocity of wave,
$v_{\text {wave }}=\lambda f \ldots \ldots(2)$
Given,
$v_{\max }=4 v_{\text {wave }}$
$y_{0} 2 \pi f=4 \lambda f$
$y_{0} \pi=2 \lambda$
$\lambda=\frac{\pi y_{0}}{2}$
Standard 11
Physics
