In the Rigid Walled Room Revisited - Part 2 episode we reviewed the solution provided by the Elmer Wave Equation solver. In that study we solved for the eigenfrequencies and eigenmodes of a rectangular room by using a first order mesh. The results we found were very accurate already, with eigenfrequencies within $1$ $\text{Hz}$ from the exact value and eigenmodes accurate within $1.4\text{%}$. However, we seen in the Mesh Order and Accuracy episode that we can significantly increase the accuracy of results by acting on the mesh fineness and, more effectively, the order. In this episode we will solve the rigid walled room eigenproblem with a second order mesh to quantify what effects this has on the accuracy of the solution.

In the Rigid Walled Room Revisited - Part 1 episode we seen how to setup an eigen system problem with Elmer by making use of the Wave Equation solver. In this episode we will review the simulation results and check the agreement with the analytical solutions in the Acoustic Modes of a Rectangular Room episode.

We covered the rigid walled rectangular room previously in the Rigid Walled Room episode. In that episode we solved for the steady state field in a rectangular rigid walled room as driven by a source placed somewhere in the room. This allowed us to see how the steady state field is sustained by a modal superposition, the purer the lower the driving frequency (assuming that this driving frequency matched an eigenfrequency of the room). The study was setup the way it was in order to work around one limitation of the Elmer Helmholtz solver: the lack of an Eigensolver feature. Had an Helmholtz Eigensolver been available we would have been able to compare with the analytical solution presented in the Acoustic Modes of a Rectangular Room episode directly, in a much more straightforward and meaningful way. It turns out that Elmer does have the capability of solving for the normal modes of cavities. This capability is implemented in the Wave Equation solver. We will explore this solver in this and further episodes, and use this solver to build a new benchmark system for the Home Studio episodes, as we mentioned in the conclusion of the Mesh Order and Accuracy episode.

In the Acoustic Modes of a Rectangular Room episode we explored the analytical model of a rigid walled room with some Julia code. We focused on finding the resonance frequencies (or eigenfrequencies) of the room and calculating the related modal patterns (eigenfunctions). Now that, thanks to The Pulsating Sphere episode, we know how to setup Helmholtz problems with Elmer we can approach the problem with the FEM method. In this episode we will solve for the modal superposition in a rectangular rigid walled room and use the results from the Acoustic Modes of a Rectangular Room episode to check the accuracy.