A transverse sinusoidal wave moves along a string in the positive $x-$ direction at a speed of $10\, cm/s$. The wavelength of the wave is $0.5\, m$ and its amplitude is $10\, cm$. At a prticular time $t$, the snap-shot of the wave is shown in the figure. the velocity of point $P$ when its displacement is $5\, cm$, is
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$v=\omega \sqrt{A^{2}-y^{2}}$
$v_{p}=2 \pi f \sqrt{A^{2}-y^{2}}$
$v_{p}=2 \pi \frac{c}{\lambda} \sqrt{A^{2}-y^{2}}$
$v_{p}=\frac{2 \pi}{0.5} \times 0.1 \sqrt{(0.1)^{2}-(0.05)^{2}}=\frac{\sqrt{3} \pi}{50}\hat j m s^{-1}$
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