Convert the wave equation from Cartesian coordinates, [ frac{partial^{2} u}{partial t^{2}}=c^{2}left(frac{partial^{2} u}{partial x^{2}}+frac{partial^{2} u}{partial y^{2}} ight) ] to polar coordinates, [ frac{partial^{2} u}{partial t^{2}}=c^{2}left(frac{partial^{2} u}{partial

Convert the wave equation from Cartesian coordinates,

\[ \frac{\partial^{2} u}{\partial t^{2}}=c^{2}\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}\right) \]

to polar coordinates,

\[ \frac{\partial^{2} u}{\partial t^{2}}=c^{2}\left(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} \theta}{\partial \theta^{2}}\right) \]

using the transformation \(x=r \cos \theta\) and \(y=r \sin \theta\).