I am looking to model the nodal surfaces in a resonating closed sphere. The sound source is external. What sort of wave equation will reveal the spherical harmonics depending on the frequency, speed of sound, sphere diameter, possibly other relevant factors?
The purpose is to make a computer simulation before attempting to visualize the nodal surfaces using neutrally-buoyant particles within the sphere (the gas might be, for example, SF6).
The wave equation for a spherical surface is given (in spherical coordinates) by
$$\frac{1}{\sin\theta}\frac{\partial}{\partial\theta}\left(\sin\theta\frac{\partial f}{\partial\theta}\right)+\frac{1}{\sin^2\theta}\frac{\partial^2f}{\partial \phi^2}=\frac{r^2}{v^2}\frac{\partial^2 f}{\partial t^2}$$
with $\theta\in[0,\pi]$, $\phi\in[0,2\pi]$, $r$ being the radius and $v$ the wave velocity. In the case of time-independence, the solutions are given by Legendre functions.
