A transverse sinusoidal wave moves along a string (18) in the positive \( \mathrm{x} \)-directio...

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A transverse sinusoidal wave moves along a string
(18) in the positive \( \mathrm{x} \)-direction at a speed of \( 10 \mathrm{~cm} / \mathrm{s} \). The wavelength of the wave is \( 0.5 \mathrm{~m} \) and its amplitude is \( 10 \mathrm{~cm} \). At a particular time \( \mathrm{t} \), the snap shot of the wave is shown in figure. The velocity of \( \mathrm{P} \) when its displacement is \( 5 \mathrm{~cm} \) is :
(1) \( \frac{\sqrt{3} \pi}{50} \hat{\mathrm{i}} \mathrm{m} / \mathrm{s} \)
(2) \( -\frac{\sqrt{3} \pi}{50} \hat{\mathrm{j}} \mathrm{m} / \mathrm{s} \)
- (3) \( \frac{\sqrt{3} \pi}{50} \hat{\mathrm{j}} \mathrm{m} / \mathrm{s} \)
(4) \( -\frac{\sqrt{3} \pi}{50} \hat{\mathrm{i}} \mathrm{m} / \mathrm{s} \)
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