Question

Select One Option Correct from the following : 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 and 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 of time, the possible expression(s) for u is (are) [Where a is a positive constant.
(A) $a \cos \frac{\pi x}{2L} \cos \frac{\pi y}{2L}$
(B) $a \sin \frac{\pi x}{L} \sin \frac{\pi y}{L}$
(C) $a \sin \frac{\pi x}{L} \sin \frac{2\pi y}{L}$
(D) $a \cos \frac{2\pi x}{L} \cos \frac{\pi y}{L}$

Answer 1

c option is correct I think.

Answer 2

Select One Option Correct from the following : 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 and 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 of time, the possible expression(s) for u is (are) [Where a is a positive constant.

(A) $a \cos \frac{\pi x}{2L} \cos \frac{\pi y}{2L}$

(B) $a \sin \frac{\pi x}{L} \sin \frac{\pi y}{L}$

✔️ (C) $a \sin \frac{\pi x}{L} \sin \frac{2\pi y}{L}$

(D) $a \cos \frac{2\pi x}{L} \cos \frac{\pi y}{L}$