quality:correction
2D standing wave with a rectangular boundary

The constants that determine the exact sinusoidal functions depend on the boundary conditions and initial conditions. To see how the boundary conditions apply, consider an example like the sheet that has been pulled taut where z (x, y, t) must be zero all around the rectangular boundary. For the x dependence, z (x, y, t) must vary in a way that it can be zero at both x = 0 and x = L for all values of y and t. As in the one dimensional example of the string fixed at both ends, the sinusoidal function that satisfies this boundary condition is