In between the 1-D wave equation for transverse waves on a string and the 3-D wave equation for longitudinal sound waves in air lies the 2-D wave equation for transverse waves on a membrane.

Here is the transverse displacement of the membrane as a function
of coordinates *x* and *y* and time *t*.

Here the speed of waves on a membrane is given by

where here

- T - is the tension per unit length in N/m, and
- - is the density per unit area in .

Tue Feb 25 21:24:33 EST 1997