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The \( (x, y) \) coordinates of the corners of a square plate are \( (0,0)(L, 0)(L, L) \) and \( (0, L) \). The edges of the plate are clamped
\( \mathrm{P} \) \( \& \) transverse standing waves are set up in it. If \( u(x, y) \) denotes the displacement of the plate at the point \( (x, y) \) at some instant
W of time, the possible expression for ' \( u \) ' is : \( [a= \) positive constant \( ] \)
(A) \( a \cos \left(\frac{\pi x}{2 L}\right) \cos \left(\frac{\pi y}{2 L}\right) \)
(B) \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{\pi y}{2 L}\right) \)
(C) \( a \sin \left(\frac{\pi x}{L}\right) \sin \left(\frac{2 \pi y}{L}\right) \)
(D) \( a \cos \left(\frac{2 \pi x}{L}\right) \sin \left(\frac{\pi y}{L}\right) \)
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