Vibrating rectangular membrane

Governed by the waveequation. No losses.
utt = c2(uxx+uyy) for 0<x<l, 0<y<L
u(0,y,t) = u(l,y,t) = u(x,o,t) = u(x,L,t) = 0
u(x,y,0) = f(x,y); ut(x,y,0) = 0
f(x,y) = x(l-x)y(L-y)

The same as above, but with
f(x,y) = x(l-x)y(L-y)cos(2pix/l)

The same as above, but with a different initial state, so that wave-propagation is easily seen. Note the inversion of the wave when reflected by the edge.