Duration: 11:45

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A sinusoidal pulse is generated at \( x=0 \) and \( t=0 \) on a string lying along \( X \)-axis. The pulse is travelling with a speed \( 1 \mathrm{~ms}^{-1} \). A rectangular pulse is generated at \( t=0 \) and is travelling in opposite direction with speed \( 1 \mathrm{~ms}^{-1} \) as shown in the figure.
The velocity of particle at \( x=9 \mathrm{~m} \) and \( t=8 \mathrm{~s} \) is
(a) \( \frac{\pi}{2 \sqrt{2}} \mathrm{cms}^{-1} \) in - y-direction
(b) \( \frac{\pi}{4 \sqrt{2}} \mathrm{cms}^{-1} \) in \( -y \)-direction
(c) \( \frac{\pi}{4} \mathrm{cms}^{-1} \) in \( +y \)-direction
(d) \( \frac{\pi}{4} \mathrm{cms}^{-1} \) in \( -y \)-direction
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