The 2-D wave equation for a membrane.

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 .

• What is a good example of a membrane?