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)`

Options

A. `a cos ((pix)/(2L)) cos((pi)/(2L))`
B. `a sin ((pix)/(2L)) cos((pi)/(2L))`
C. `a sin ((pix)/(L)) cos((pi)/(L))`
D. `a sin ((2pix)/(L)) cos((pi)/(L))`

Answer

C

Explanation

The possible expression will be one which gives zero displacement a x = 0, X = L, y = 0 and y = L.