Rectangular Rooms and Resonant Modes - Tip 9

Every realistic room (with the exception of a perfect anechoic chamber) has a set of resonant frequencies. These frequencies and how much they boost the sound level at the resonant frequencies are defined by the room geometry and the surface materials. In rectangular rooms, as well as most other rooms, the mode density increases rapidly with increasing frequency.

The coloration of sound caused by the modal resonance depends on the spacing of the modes in frequency and how much the modes are excited by loudspeakers. Only if the room dimensions are smaller than half the sound wavelength no mode can exist, and sound pressure in the room depends only on the loudspeaker output capability.

Frequencies below about 300 Hz are the most critical: there the density of modes is fairly small, with wide spacing between the modes. This makes the modes audible because they do not overlap and absorbing the resonant energy is difficult at low frequencies. Also, large rooms have a higher mode density than small rooms. This favors using a larger space, as long as the reverberation time of the space remains sufficiently low.

The exact distribution of the modes also depends on the relative proportions of the room dimensions. The worst case is a cubical room. There the identical dimensions lead to a coincidence of the three axial sets of modes, and the mode resonances along the three axes of the room amplify each other. As a general rule, one should avoid precise integer ratios in room dimension proportions. Now we already begin to see that using small rooms involves some acoustical compromise.


tip9 fig1



tip9 fig2



tip9 fig3


Figure – Modal density can be increased by selecting the right proportions for the room dimensions. Top: 27 m3 room with 1:1:1 ratio. Middle: 27 m3 room with 1.54:1.28:1 ratio. Bottom: 200 m3 room with 1.54:1.28:1 ratio.