Wave motionHardBloom L3
Question
The (x , y) co-ordinates of the corners of a square plate are (0, 0) (L, 0) (L, L) & (0, L). The edges of the plate are clamped & transverse standing waves are set up in it . If u (x, y) denotes t he displacement of the plate at the point (x, y) at some instant of time, the possible expression(s) for u is/are: (a = positive constant)
Options
A.$a\cos\left( \frac{\pi x}{2L} \right)\cos\left( \frac{\pi y}{2L} \right)$
B.$a\sin\left( \frac{\pi x}{L} \right)\sin\left( \frac{\pi y}{L} \right)$
C.$a\sin\left( \frac{\pi x}{L} \right)\sin\left( \frac{2\pi y}{L} \right)$
D.$a\cos\left( \frac{2\pi x}{L} \right)\sin\left( \frac{\pi y}{L} \right)$
Solution
Sol. As all the edges of the plate are clamped, So all the points on each edge will be nodes.
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