In the Home Studio - Part 3 and Home Studio - Part 4 episodes we referred to the results of our frequency sweep as frequency responses. In those episodes we calculated the steady state pressure disturbance in a room at different frequencies and sampled the field at a couple of locations so to be able to plot the steady state magnitude at those locations as a function of frequency. It is intuitive to refer to this result as a frequency response, in the sense that the field magnitude as a function of frequency gives us an understanding of how strong the steady state disturbance is at any given frequency in our study. However, what is typically meant by by frequency response is in reality quite a different concept. This episode is intended to provide a cursory introduction to this concept, and explain why what we calculated in the previous episodes is different, even though we called it frequency response.

In the Home Studio - Part 3 episode we simulated the steady state pressure field for a realistically shaped room governed by the linear wave equation. The boundary condition for the room was that of ideally rigid walls. We seen that the effect of such a boundary condition is an extremely uneven frequency response. This due to how sharp the resonances of the room are. In this episode we will introduce slightly more realistic boundary conditions and see what the effect on the solution is.

In the Home Studio - Part 1 episode we gave a first look at the response of a realistically shaped room with rigid walls. We understood how to develop and run a model with an uniform velocity sphere source placed somewhere in the room. We run the model up to $400$ $\text{Hz}$ with the help of the convergence considerations outlined in the Dealing with Convergence Issues episode. In the Home Studio - Part 2 episode instead we used Elmer’s WaveSolver to compute the eigenmodes of the room. Not only that, but we introduced several improvements such as the use of $p$-elements and locally refined meshes. In this episode we will model in high detail the low frequency response of our room, up to $125$ $\text{Hz}$, making use of the improvements we just mentioned.