This simulation attempts to recreate the distribution of sound in square concert halls. The set-up is seen in the figure below, where the radii are calculate through geometry

The radii come out to be

$$\begin{aligned} r_1 &= d_1 \sqrt{\left(\frac{y}{2d_1-x}\right)^2 + 1} \\ r_3 &= d_3 \sqrt{\left(\frac{y}{2d_1+x}\right)^2 + 1} \\ r_2 &= \sqrt{\left(\frac{y(2d_1-x)}{d_1}\right)^2 + (d_1 - x)^2} \\ r_4 &= \sqrt{\left(\frac{y(2d_1+x)}{d_1}\right)^2 + (d_1 + x)^2} \\ r_5 &= \sqrt{x^2 + y^2} \end{aligned}.$$

Then, the sound level is found through $$\beta = \log{\left(\frac{I}{I_0}\right)}$$ where $I$ is the intensity and $A$ is amplitude of each (total) sound wave. An example result of the code is this image!

An absorbtion can also be simply applied through the absorption coefficient $\alpha = I_{\alpha} / I$ which results in this:

An $\alpha$ of $1$ implies that everything is being absorbed into the walls of the hall, removing the interfering waves completely, which is what is seen in the figure.