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 ((pi x)/(2L)) cos ((pi y)/(2L))`
B. `a sin ((pi x)/(L)) sin ((pi y)/(L))`
C. `a sin ((pi x)/(L)) sin ((2pi y)/(L))`
D. `a cos ((2pi x)/(L)) cos ((pi y)/(L))`

Answer

B, C