Physics

Problem

The

(x, y)

co-ordinates of the corners of a square plate are

(0, 0)

(L, 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(\pi x/2L) \cos(\pi y/2L)

a \sin(\pi x/L) \sin(\pi y/L)

a \sin(\pi x/L) \sin(2\pi y/L)

a \cos(2\pi x/L) \sin(\pi y/L)