A 40 Hz soundwave has a wavelength of 8.5 meters:
speed of sound at sea level = 340.29 m/s
340.29/40 Hz = 8.5
8.5/4 = 2.125 meters
How are you getting mutual coupling with the 1/4 wavelength theory if your subs are 5 meters apart? They would need to be no more than 2.125 meters apart for 1/4 wavelength coupling at 40 Hz.
Of course, not everyone agrees that 1/4 wavelength is the distance needed for mutual coupling. Some think that 1/2 wavelength spacing is required. This is from the Genelec website:
When two or more subwoofers (except the 7050B as it does not have a sum output) are positioned close to one another mutual coupling is the fortunate by-product. This is due to the long wavelengths, associated with low frequencies, causing constructive superimposition. For mutual coupling, the subwoofers must be placed within ½ a wavelength of one another (85 Hz upper crossover frequency ½ wavelength is approximately 2 m). For example, two subwoofers give a 6 dB increase in acoustical output at the listening position
Here is another interesting discussion on "coupling" of drivers from the Rane website:
coupling or mutual coupling Loudspeakers. General term describing the combining behavior of two or more drivers reproducing the same frequency. If two or more identical loudspeakers are mounted such that their acoustic centers are close together (i.e., some fraction of a wavelength), their acoustic outputs over some frequency range will combine (couple) and propagate forward as one waveform, thus two smaller drivers behave as one big driver. [This is the simple vague answer, a detailed specific answer requires a great deal more.]
Mark Gander, VP of pro marketing for JBL, puts it this way: "The correct maximum distance that mutual coupling occurs depends on what you want to define as the limit of coupling. For example, is it the maximum approaching +3 dB, or when it reverts to unity gain? It's a gradual transition, so either 1/4 wavelength or 1/2 wavelength separation distance is just a rule of thumb." [Gander sites Lee Henney's Radio Engineering Handbook, 5th ed., Ch. 11 'Loudspeakers and Room Acoustics,' as a useful source that shows the response from groups of pistons at various distances, following the work of Klapman (Klapman, S. J., "Interaction Impedance of a System of Circular Pistons," J. Acoust. Soc. Am., vol. 11, p. 289, 1940.)"
John Murray, Digital Audio Lab Manager, Columbia College Chicago, explains: "Mutual coupling is when multiple drivers produce relatively more output at the low end of their response curve than a single driver. This occurs when the drivers are close enough together to have less than 90 degrees of path length difference for the wavelengths of interest at a given listening position. This phenomena is position-dependant, and is, in fact, what causes the high level portion of lobing. At shorter wavelengths (higher frequencies) and listening positions farther off-axis of the drivers, the phase difference becomes destructive which results in the nulls of lobing. Even with drivers that are touching, mutual coupling over a wide listening area are virtually always below 300-500 Hz.
Chuck McGregor, Technical Services Manager for EAW, says, "It depends." And goes on to explain: "There is no such thing as a correct, maximum source spacing distance for mutual coupling. First one has to define what they consider as mutual coupling (i.e., at what level off-axis does one stop considering the sources as no longer being mutually coupled) and then what is the criteria is for a particular situation, meaning the frequency to which one requires the coupling and the overall angle over which it is needed. Based on this stuff you can figure out the maximum, acceptable driver spacing.
Harry Olson analyzes this (although he does not call it mutual coupling) as a double or doublet source in his book, Acoustical Engineering, section 2.3.
McGregor's personal view: "First, mutual coupling will occur on-axis even if the center-to-center distance of two sources is 100 light years. At 1/2 wavelength separation they cancel completely at 90 degrees off-axis. At 45 degrees off-axis the signal is roughly 6 dB down, i.e. the equivalent of one source. Does this mean their mutual coupling beamwidth is limited to 45 degrees or is it limited at the 6 dB down point? Maybe it is 3 dB down over a lesser angle?"
McGregor offers this as a detailed definition: "Mutual coupling is when the outputs of two or more acoustical sources producing the same signal combine (couple) and propagate forward as one waveform. In this way, two smaller drivers can behave as one larger driver. While any number of sources can mutually couple, for clarity this discussion will focus on two sources.
The amount of coupling directly on axis between two sources producing the same signal will result in a 6 dB increase in level. On-axis, the spacing of these sources has absolutely no effect on this result. However, because the two sources must be physically separated, the coupling decreases off axis as the path lengths from each source to the listener increasingly differ. This is because the two waveforms become increasingly out of phase. For a given source spacing, the higher the frequency is, the more quickly off-axis this occurs. Likewise for a given wavelength (frequency) the wider the source spacing, the more quickly off-axis this occurs. Thus, the amount of mutual coupling at any point off-axis depends on both the source spacing and the wavelength (frequency) of the sound being produced.
What is considered mutual coupling? The broadest definition is that any multiple sources producing the same signal whose outputs acoustically combine to produce an increase in level over that of one of the sources means mutual coupling is taking place.
For audio purposes, changes of 3 dB and 6 dB are often used as typical criteria for acceptable increases or reductions in level. For two sources, a 3 dB decrease from the on-axis coupling of 6 dB occurs when the path length difference from the sources to the listener is 1/4 wavelength. This equals a 90 degree phase shift between the two waveforms. Likewise for two sources, a 6 dB decrease from the on-axis coupling of 6 dB occurs when the path length difference from the sources to the listener is 1/3 of a wavelength. This equals a 120 degree phase shift between the two waveforms. It also results in a level that equals the output of one source, meaning the amount of mutual coupling is effectively equal to zero.
Thus, the best definition for mutual coupling is defined by what is acceptable for any given situation. This can vary from the full, on-axis mutual coupling to the effective absence of mutual coupling, which is where the level decreases to be equal to or less than of one of the sources. Contrary to popular notions, there is no particular driver spacing that results in mutual coupling. Mutual coupling is defined by the level below which mutual coupling is not longer considered mutual coupling. This is an arbitrary level but, in any case, it cannot be below the level of one of the sources. The source spacing and the wavelength (frequency) of the signal then determines the angle over which the combined wavefront falls within the chosen definition of being mutually coupled."http://www.rane.com/par-c.html
And another one from the ServoDrive manual:
If you are using more than one ServoDrive subwoofer for an application, coupling the subwoofers by placing them next to each other will result in a large increase in efficiency and extended low frequency response. Coupling ServoDrive subwoofers in this manner has the effect of creating a larger, more powerful single sound source equivalent to a much larger subwoofer. Units may be placed at a desired wavelength apart from each
other to effectively create "lobes" of sound where the output would resemble a large figure 8, with little output to the sides, yet projecting a large output to the front and rear.http://www.servodrive.com/Download_f...BassManual.pdf
Finally, see "Low Frequency Augmentation - Subwoofers" starting on Page 26 of this article from the JBL Pro Sound Systems Design Reference Manual:http://www.jblpro.com/pub/manuals/pssdm_2.pdf
Paul Scarpelli said it:
Putting a good speaker in a horrible room is like driving a Porsche 911 on glare ice, and then blaming the lack of handling on the car.