A standing wave pattern of amplitude A in a string of length L shows 2 nodes (plus those at two ends). If one end of the string corresponds to the origin and \( v \) is the speed of progressive wave, the disturbance
\( \mathrm{P} \) in the string, could be represented (with appropriate phase) as:
(A) \( y(x, t)=A \sin \left(\frac{2 \pi x}{L}\right) \cos \left(\frac{2 \pi v t}{L}\right) \)
(B) \( y(x, t)=A \cos \left(\frac{3 \pi x}{L}\right) \sin \left(\frac{3 \pi v t}{L}\right) \)
(C) \( y(x, t)=A \cos \left(\frac{4 \pi x}{L}\right) \cos \left(\frac{4 \pi v t}{L}\right) \)
(D) \( y(x, t)=A \sin \left(\frac{3 \pi x}{L}\right) \cos \left(\frac{3 \pi v t}{L}\right) \)
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