Room response to low frequencies consists entirely of a set of very sharp resonances at different frequencies. For a perfectly rectangular room, this set of resonances can be easily calculated. In a perfectly solid lossless room with ideal reflecting surfaces, the room will only respond to these resonant frequencies. Excitation at a frequency that is not matched with a room mode will only excite nearby modes and the excitation frequency will not be present. The sound will also ring for an infinite period of time in a lossless environment.

Each resonant frequency is known as a mode of vibration. Any room contains many modes of vibration, it is the number of modes of vibration and their spacing that determines the quality of response.

Larger rooms contain more modes of vibration within a given frequency range than smaller ones. This increased modal density in larger rooms is directly responsible for the fact that larger rooms give a better bass response.

A room can be considered similar to a large musical instrument such as a pipe organ. A room with poorly distributed resonances is similar to having a pipe organ with some of the pipes actually missing. An overly excited room mode is similar to having a single pipe in the organ play much louder than all the rest.

In real rooms losses such as openings and absorption in furniture and walls lower the Q* (sharpness) of the resonances that characterize the room frequency response. This effect of losses on the frequency domain room response is illustrated below.

In a rectangular shaped room the loudspeaker must be placed in the corner to excite all of the modes (pipes) that characterize the response of the room. In some occurrences, one or more modes will be overly excited with corner placement of subwoofers. This can cause the "boomy" response, refered to as room boom, and characterized by low frequency ringing.

A popular way of dealing with this room boom is to place the subwoofer in a location other than the corner to eliminate excitation of problem modes of vibration.

For a high fidelity application, it is desirable to excite all room modes to obtain the smoothest and best sounding bass response. This is only accomplished by placing a single subwoofer in a corner in the case of rectangular shaped rooms. Overly excited room modes may require correction with bass traps or helmholtz resonators. These devices selectively absorb low frequencies to increase losses in the room at frequencies that become over excited. This is similar to reducing the level of a pipe in the organ to match the level of the others.

For typical home theater and home hifi applications, the building and tuning of helmholtz resonators may be impractical. This method requires much trial and error and is not viable for the inexperienced. Our recomendations for most applications is to place the subwoofer in various places near the corner and take multiple measurements to compare results and find the best location. The project example illustrates this.

Parametric equalizers may be used to accomplish the exact same thing as what would be accomplished using a passive device such asa helmholtz resonator but this ideal solution is difficult due to the lack of affordable equalizers and the high end sectors reluctance to accept electronic equalization as a viable alternative.

One other solution to low frequency room response problems is to add more losses. Big heavy furniture placed in the room, openings (particularly near corners) and walls with thin wood panelling all serve to increase losses in the low frequencies and therefore have a smoothing effect on the overall bass response.

Room modes consist of three different types of resonances, these are known as axial, tangential & oblique modes. Axial modes consist of waves resonating only along one dimension: the length, width or height of the room, Tangental modes involve two dimensions, the length & width, length & height, or width & height. Oblique modes involve all three dimensions in each mode of resonance. Normally the axial modes have the most strength while the oblique modes have the lowest strength. Often times the oblique modes are ignored in simple analysis. Axial modes are the ones that most often become overly excited and require correction using an equalizer or resonators.

An example of an axial mode would be that formed along the length of our example room, the first axial mode along the room length is: SpeedOfSound/(2*RoomLength) = 1130/(24.66*2) = 23 Hz. Additional modes would exist at integral multiples of 23 Hz : 46 Hz, 69 Hz, etc. The width dimension gives a first axial mode at 1130/(19.66*2) = 28.7 Hz, 57 Hz, etc. This room does not have the ideal cubical shape assumed due to some of the ceiling being lower than the 7'8" specified to cover heating ductwork, and the fact that these rooms are never built perfectly square. This is therefore a slightly asymmetrical shape that causes some of the modes to be slightly shifted from the calculation results in measurement. The room in this discussion was found to have two modes that were overly excited: 33 Hz and 63 Hz. Neither of these modes will appear in calculation because of the non ideal rectangular shape and other effects not included in the calculation. There would be little value in calculating the remaining modes of vibration for this room.

If one subwoofer is placed in one corner, the following axial modes of vibration will be excited due to the width of the room: 28.7 Hz, 57.4 Hz, 86.1 Hz, 113.5 Hz, etc. Other modes will be excited as well, but the point here is that if another subwoofer is added to a room with these modes in the other corner as shown in the room layout, the modes at 28.7 Hz and 86.1 Hz would cancel and no longer exist in the response of the room. The modal density will be lower, the room response will contain more null frequencies and the overall bass response will not be as subjectively smooth. This cancellation does not completely occur in practice because of the deviation from perfect room symmetry, but the phenomenon does exist and is audible.

* Q is a number that indicates the "quality" of a resonance and dates back to the old days of tube radios. The higher the Q, the sharper the resonance. In room acoustics, sharp resonances are not desirable, but in the old tuning circuits for radios, a sharp resonance was desireable to pick up a radio station with little interference from adjacent stations on the dial.