Modal problems in nonrectangular rooms

The acoustic behavior of the low frecuency of a rectangular enclosure, is very simple using the Rayleigh formula:

f_k,m,n = 172,5 . √((k/L_x)²+(m/L_y)²+(n/L_z)²)

where L_x, L_y and L_z represent the room in meters, k, m, n are integer values (0, 1, 2, 3, ...)

Knowing the behavior at low frequency of a room is crucial in critical listening spaces such as control rooms of a recording studio. Understanding where and how these standing waves appear, is necessary to design appropriate materials for each case, as well as its optimal placement. In the same way, a thorough knowledge of this frequency range, allows to define optimum listening position and the monitor placement.

When one or more of the surfaces are splayed, loosing the rectangular shape, the modal problems do not disappear, they simply move and frequency shift, which makes it harder to predict. In these cases we'll need to use numerical approach mathematical tools such as finite element techniques, which allow solving the Helmholtz integral radiation problem.

In the figure above you can see an example of the sound pressure change in a rectangular room and a nonrectangular at 63Hz, both with the same area and volume, with two 0.1Pa ideal pressure sources.