Background
The two-dimensional wave equation is given by:
$\frac{\partial^2 u}{\partial t^2} = c^2 \left(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\right)$
The wave equation can be used to represent the response of a rectangular membrane. A
rectangular membrane of sides $a = 4$ m and $b = 8$ m, $c^2 = 1$, initial deflection $f(x, y, 0) =
\sin\left(\frac{3\pi x}{4}\right)\sin\left(\frac{\pi y}{2}\right)$, and zero initial velocity is given.
Tasks
In group consisting of 2 or 3 members:
i. Determine the response of the membrane $u(x, y, t)$ using the Fourier series method;
ii. Plot the response of the membrane; and
iii. Comment and show how the response can be increased without changing the initial
conditions.
