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

Answer

B, C

Explanation

Due to the champing of the square plate at the edges, its displacements along the `x-` and y-axes will individually be zero at the edges. Only the choices (b) and ( c) predict these displacements correctly. This is because `sin 0 =0`.