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A transverse sinusoidal wave moves along a string in the positive \( \mathrm{x} \)-direction at a speed of \( 10 \mathrm{~cm} / \mathrm{s} \). The wavelength
\( \mathrm{P} \) of the wave is \( 0.5 \mathrm{~m} \) and its amplitude is \( 10 \mathrm{~cm} \). At a particular time t, the snap-shot of the wave is shown in
W figure. The velocity of point \( \mathrm{P} \) when its displacement is 0.05
[IIT-JEE 2008]
(a) \( \frac{\sqrt{3} \pi}{50} \hat{j} m / s \)
(b) \( -\frac{\sqrt{3} \pi}{50} \hat{j} \mathrm{~m} / \mathrm{s} \)
(c) \( \frac{\sqrt{3} \pi}{50} \hat{i} \mathrm{~m} / \mathrm{s} \)
(d) \( -\frac{\sqrt{3} \pi}{50} \hat{i} m / s \)
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