Examples of 2D wave equations with analytic solutions I need to numerically solve the following wave equation$$\nabla^2\psi(\vec{r},t) - \frac{1}{c(\vec{r})^2}\frac{\partial^2}{\partial t^2}\psi(\vec{r},t) = -s(\vec{r},t)$$ subject to zero initial conditions $$\psi(\vec{r},0)=0, \quad \left.\frac{\partial}{\partial t}\psi(\vec{r},t)\right|_{t=0}=0$$ where $\vec{r} \in \mathbb{R}^2$ and $t \in \mathbb{R}$.
The problem is that I don't know if my numerical solution is right or not, so I wonder if there are some simple cases where the analytic solution can be calculated (besides the green's function, i.e. the solution when $c(\vec{r}) \equiv $ const and $s(\vec{r},t) = \delta(\vec{r},t)$), so I can compare it with my numerical solution. 
Thanks!

Solution using Green functions and using Sommerfeld radiation condition, in cylindrical coordinates. 
\begin{eqnarray}
u_s(\rho, \phi, t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} \{ -i \pi H_0^{(2)}\left(k | \sigma - \sigma_s| \right) F(\omega) e^{i\omega t} d\omega\}
\end{eqnarray}
Where $s$ denotes the source position.
More details and implementation can be found in this post here from Computational Science.It uses the following reference: Morse and Feshbach, 1953, p. 891 - Methods of theoretical physics: New York, MacGraw-Hill Book Co., Inc. 
Here are two snapshots $\mathbb{R}^2$ in [200, 200] lattice with space increment of 100 meters (is not in the axis), velocity 8000 m/s.

The source function $ s(\vec{r},t) = \delta(\rho, \phi)f(t) $ bellow sampled with $\Delta t = 0.05 $ seconds, obviously placed in the origin $(\rho=0,\phi=0)$. In fact can be anything you want as long you can have its Fourier Transform.
 
