 Vibrating membrane

A physical sheet under uniform isotropic tension per unit length T and with mass per unit area $\rho$ has small transverse displacement satisfying ${\partial }_t^2\psi =c^2{\nabla }^2\psi$, where $c^2=T/\rho$. Fixed edges impose zero displacement. This mechanical membrane model neglects bending stiffness, large slopes and dissipation.