Question

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of $10cm/s$. The wavelength of the wave is $0.5m$ and its amplitude is $10cm.$ At a particular time $t$, the snap shot of the wave is shown in figure. The velocity of point P when its displacement is $5cm$ is

• A. $\frac{\sqrt{3}\pi }{50}\hat{j}m/s$
• B. $-\frac{\sqrt{3}\pi }{50}\hat{j}m/s$
• C. $\frac{\sqrt{3}\pi }{50}\hat{i}m/s$
• D. $-\frac{\sqrt{3}\pi }{50}\hat{i}m/s$

Answer 1

The correct option is A $\frac{\sqrt{3}\pi }{50}\hat{j}m/s$

$Y=5$ and $v$ is +ve

$Y=A\sin (\omega t+\varphi ),v=A\omega \cos (\omega t+\varphi )$

form above equation we get $\omega t+\varphi =\pi /6$

$\omega =2\pi \mu /\lambda =2\pi /5$

so $v=A\omega \cos (\omega t+\varphi )=\pi \sqrt{3}/50$