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The (x, y) co-ordinates of the corners o...

The `(x, y)` co-ordinates of the corners of a square plate are `(0, 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) `(a = positive constant)`

A

`a cos ((pix)/(2L))cos ((piy)/(2L))`

B

`a sin ((pix)/(L))sin ((piy)/(L))`

C

`a sin ((pix)/(L))sin ((2piy)/(L))`

D

`a cos ((2pix)/(L))sin ((piy)/(L))`

Text Solution

Verified by Experts

The correct Answer is:
C
The possible expression will be one which gives zero displacement at `x=0,X-L,y=0` and `y=L`.
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