A sinusoidal pulse is generated at \( x=0 \) and \( t=0 \) on a string lying along \( X \)-axis....

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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 displacement of the particle at \( x=9 \mathrm{~m} \) and \( t=8 \mathrm{~s} \) is
(a) \( \sqrt{2} \mathrm{~cm} \)
(b) \( \frac{3}{2} \mathrm{~cm} \)
(c) \( (\sqrt{2}+1) \mathrm{cm} \)
(d) \( \left(\frac{\sqrt{2}+1}{\sqrt{2}}\right) \mathrm{cm} \)
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