# Acoustics of Mutual Coupling

Discussion in 'Amps and Cabs [BG]' started by MikeyD, Aug 19, 2001.

1. ### MikeyD

Sep 9, 2000
Hi - I'm forwarding a private message from FalseHoodBass asking me about mutual coupling of loudspeakers. His remarks are shown with FHB, and mine are in bold.

FHB: hey... i get the basic idea of mutual coupling.. i was wondering if you could answer some questions i have.
ok.. it occurs when the speakers are within 1 wavelength? 1/4 wavelength from each other?

As I recall (and it makes a lot of sense to me), the effect occurs when sources are within 1/4 wavelength.

FHB: i assume this is the center of the speaker that the distances are measured from?

I would assume this first, even though in a microscopic sense it probably occurs between the radiating surfaces - even at the edge of drivers. It's probably safer to consider it from center to center. However, I'm not clear on it, because the mathematics of what's going on is very messy, and it would take a long time for me to sort it out. This phenomenon is multidimensional.

FHB: am i correct in assuming that and 810 gets better bass response than a 410 because of mutual coupling?

All else being equal, I'd expect the 810 to do a bit better. I suspect the "mutual coupling" effect is wrapped up in the geometry of the cabinet as well, because the effective radiating surface depends on diffraction, which depends on the driver, the shape, and the size of the cabinet. This gets into very messy acoustical physics, and I'm not really up on it these days. I would also expect a 4x10 in a large cabinet (but with the same chambered internal volume) to do slightly better than its counterpart in a smaller cabinet - for these same reasons.

FHB: If it's say 5 feet high, the top and bottom speakers are about 4 feet apart, and the wavelength of the fundamental on a low b is 10 meters (just over 30 feet) long

At room temperature, the 31 Hz. wave of low B is about 36 feet long. A quarter wave would be 9 feet, which would envelop the entire cabinet.

FHB: it seems that the same idea could also be used to produce phase cancelling at certain frequencies... think young's double slit experiment for sound... and that seems like it would be undesireable....

Your bringing up interference sources is close to the mark. You remember how interference patterns are set up from those two sources, which is excellent. You are starting to touch on the topic of array phasing. The 8x10 (or any set of multiple drivers) forms an array, and most certainly directionality is affected by phasing of sound arriving at particular points in space from the different drivers.

In fact, such phasing occurs even from a single driver - if you think of the single cone as an amalgam of a zillion microscopic surfaces. It is such phasing, through the physics of diffraction, that gives the speaker its directivity characteristic vs. frequency. Note that the hypothetical point source (a speaker whose size is tiny compared to the wavelength it is producing) has no directivity so radiates omnidirectionally. On the other end of the spectrum, if the driver is large compared to the wavelength, the sound radiated from one part of it interferes with that from another. Then (to add to the confusion), if the cone is not entirely radiating in phase (as a unit), there are other anomalies that occur. The "doubling" or modal vibration of the cone at certain frequencies causes parts of it to be out of phase with other parts, which adds to the complexity of the radiation pattern and frequency response.

FHB: Is mutual coupling an all or nothing thing?

No. I'm sure the answer is no - the physics involved do not lend themselves to discontinuous (i.e., yes/no, on/off) behavior. It's more of a gradual effect.

FHB: I've heard that it doubles the power in a certain direction (+3dB), but does it fall off gradually for higher frequencies and speaker distances, or just stop altogether? it seems that this "shelving" effect would also be undesireable if one is experiencing too much power below the mutual coupling frequency...

You can think of it as having the same kind of effect as placing your speaker near a corner. There will be augmentation of the lower frequencies, and sometimes it can be undesirable.

FHB: sorry if im asking too much.. but i know you have technical knowledge of this stuff.. if this is too much.. just let me know and i'll post it as a thread.

They are good questions, and I like to help when I can. It's nice to see people like you being curious about these things! I hope my reply helps.

If anyone else has some good insights, they would be welcome.
- Mike

2. ### steinbergerxp2Guest

Jul 11, 2001
Even if I don't grasp the underlying physics completely, it's always nice to read a discussion on cabinet design, that doesn't rely on the words "warm", and "punchy".

3. ### Joris

Hold those thoughts, Mike! This sounds like a good FAQ topic. Pretty in-depth, but nevertheless valuable info. People who don't wanna read it, just skip it.

4. ### FalsehoodBass

Jul 22, 2001
Denver, CO
hey thanks for all the in depth info... i really don't have anything else to ask...am i right in assuming that in order for it to occur that the speakers don't have to be the same size, hence a 410+ 15/18 config can still benefit?

ok i have a related question.. what about direction? Understandibly higher freaqencies are more directional than lower ones (diffracting wavelenghts etc.) But what angle can i assume that my entire frequency range will be heard? I usually draw a 90 degree angle from the center of my 810 cab and assume everyone within that can hear me pretty well, is that about right?
Thanks again for any help and info...

5. ### MikeyD

Sep 9, 2000
Yes - it would be good to put into your TB FAQ/Encyclopedia! However, you probably noted that I'm on a bit of shaky ground, because this is a rather complex and difficult-to-understand phenomenon. I don't really know that much about it at this time. I would have to do a lot of hard reading and math to gain to an authoritative viewpoint on this subject.
- Mike

6. ### MikeyD

Sep 9, 2000
As I recall, you are studying physics, so maybe all this will turn you on to acoustics enough that sometime YOU'LL be the resident acoustics expert! Anyway - yes, if the speakers are reproducing the frequency of interest whose wavelength is around 4x the distance between the drivers, there should be some degree of mutual coupling. I have serious reservations about assuming a fixed number, such as 3 dB boost, though. I suspect there are a lot of dependencies, and 3 dB is probably the *maximum possible* boost.

Because of the interference/diffraction phenomena we discussed earlier, if you pick any one point in an anechoic (i.e., no echoes/reverberation - or totally dead) space, I expect that some frequencies will totally cancel themselves at that point. It's sort of a spatial comb filtering effect. You can readily hear the flip side of this if you put a fairly high frequency (say 2 kHz) into a good-sized woofer and move about near the front of it: you can hear the tone weave in intensity. If, on the other hand, you don't move but vary the frequency, I expect the same effect.

In my view, room acoustics tend to squish out some of these effects, yet also exacerbate others - such as standing waves. It become extremely difficult to get an absolutely flat response across the entire spectrum unless you are using a driver whose size is small compared to the shortest wavelength and you're in an anechoic environment.

The quick answer to your question: higher frequencies tend to be more directive from loudspeakers, so you would want to position the speakers so most of the intended audience is straight in front. Many manufacturers show generalized directivity "spreads" (or beamwidth). A PA speaker might claim 30-degree coverage over most of its operating range - so you try to set the speaker back far enough and point it so that most of the audience lies within that 30 degree beam. Fortunately, bass cabinets are more forgiving because most of the energy coming out of them is much lower in frequency and tends to be less directional. It is quite common for people to hear the bass all over the place. (Nice rhyme, huh?) But byproducts of picking or slapping might get muffled off-axis.

- Mike

7. ### FalsehoodBass

Jul 22, 2001
Denver, CO
once again.. thanks for the info... that was your 666th post....

8. ### bgavin

May 3, 2001
Orangevale, CA 95662
The JBL Sound Design manual quotes mutual coupling at +3 dB "due basically to the tendency for the two drivers to behave as a single unit with a larger cone diameter, and hence higher efficiency." There is a roll-up curve at the point where mutual coupling begins to occur at 1/4 wavelength between drivers, and it remains at a flat +3 dB at lower frequencies.

Each successive mutual coupling occurs at 0.7x of the previous mutual coupling frequency. For example, two drivers are mutually coupled at 100 Hz. Adding another pair for a total of 4 drivers, the combination mutual coupling effect occurs at 70 Hz. This downward progression is the limiting factor to mutual coupling.

Assuming a 12" center to center distance between drivers in a typical 4x10 cabinet as 1/4 wavelength, a 48" wavelength is 282 Hz. The first pair of drivers would couple at 282 Hz, and the combined set of 4 drivers would couple at 197 Hz (282 * 0.7). This is everything from the high G string, 12th fret and lower.