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View Full Version : Does mutual coupling come in to play when subwoofers are in different area of a room?



wsilva
02-01-2011, 07:46 PM
If I understand correctly, when 2 subwoofers are placed near each other the efficiency of the system goes up by 3db (please correct me if I am wrong), and would go up another 3db if another sub was added to the stack.

What I am wondering, is if multiple subs were used but were placed in seperate areas such as one in each corner of the room would the efficiency go up in a similar way?

Second question if any one wants to help, is if multiple subs raise the efficiency of the system, wouldn't less amplifier power be required to reach the same sound level?

Say if it took a good 500 watt amp to run a single sub in a room, would by going to 4 subs would you need a much less powerful amp to drive to the same sound level?

Thanks for any help in explaining how this works.

Eaulive
02-01-2011, 09:32 PM
If I understand correctly, when 2 subwoofers are placed near each other the efficiency of the system goes up by 3db (please correct me if I am wrong), and would go up another 3db if another sub was added to the stack.

Yes to the first part, no the the second :)
Each time you double the amount of speakers you go up 3dB, not each time you add a speaker. So if you have one it goes up 3dB for one more, but then only another 3dB for two more, then another 3dB for four more, etc.


What I am wondering, is if multiple subs were used but were placed in seperate areas such as one in each corner of the room would the efficiency go up in a similar way?

If you receive the same amplitude at the same phase from both subs, yes, but it's seldom the case at every point in the room, usually there's only one sweet spot where this effect takes place.
If you receive energy from the speakers at different phases (distance from source affect phase) you could have exactly the opposite effect: a cancellation.

It could also be a gain at some frequencies and a cancellation at others, leading to what we call "comb filtering"


Second question if any one wants to help, is if multiple subs raise the efficiency of the system, wouldn't less amplifier power be required to reach the same sound level?

Say if it took a good 500 watt amp to run a single sub in a room, would by going to 4 subs would you need a much less powerful amp to drive to the same sound level?

Nope, there's 3dB increase when doubling the number of speakers assuming both speakers are driven to the same amplitude (voltage), so if you have one amplifier driving 28V into an 8 ohms woofer, the amp is delivering 100W to the load.
If you connect another speaker to the same amplifier and have the same 28V into both (3dB increase), then the load will be 4 ohms and the amplifier will be delivering 200W to the load.
If you reduce the power by half to go back to 100W, you reduce the SPL by 3dB and you're back where you started. :)

The advantage is that your subs are working half as much, so less distortion, less stress.

wsilva
02-01-2011, 11:16 PM
Many thanks for the excellent reply:)

The cancellation and comb filtering are especially interesting points.

Regards

Hoerninger
02-02-2011, 07:56 AM
http://www.zainea.com/mutualcoupling.htm
____________
Peter :confused:

badman
02-02-2011, 08:34 AM
http://www.zainea.com/mutualcoupling.htm
____________
Peter :confused:
Not gonna read that because it hurts my eyes, but it's pretty simple. At wavelengths where spacing is less than approx 1/4 WL you can assume 3dB summation increase for a given POWER (watt) input, this is EFFICIENCY gain. For a given VOLTAGE input, you can gain 6dB SENSITIVITY total if you wire in parallel, as the power input goes up by a factor of two (same voltage, double current due to half the impedance), so 3dB from doubled current and 3dB from the efficiency of multiple drivers (mutual coupling). Likewise, you can wire in series and you gain 3dB of efficiency from twice the cone area (and box), but lose 3dB of sensitivity due to the doubled impedance (halved current), leaving you with +3 -3 or a net SENSITIVITY change of 0, but a 3dB EFFICIENCY change.

Just keep in mind that efficiency always goes up by 3 with a doubling of drivers (and boxes) and that efficiency is one component of sensitivity, the other being the ratio of impedance for the multidriver to the impedance for a single, as that controls the current for a given voltage and thus the power input for a given voltage, and sensitivity is stated in voltage, where efficiency is stated in wattage.

Of course, for subs that aren't close together, you have modal behavior dominating the frequency response and summation is not at all coherent- this is a good thing because you can significantly smooth the response using multiple, non-colocated, subs.

Eaulive
02-02-2011, 09:38 AM
At wavelengths where spacing is less than approx 1/4 WL you can assume 3dB summation increase for a given POWER (watt) input, this is EFFICIENCY gain. For a given VOLTAGE input, you can gain 6dB SENSITIVITY total if you wire in parallel, as the power input goes up by a factor of two (same voltage, double current due to half the impedance), so 3dB from doubled current and 3dB from the efficiency of multiple drivers (mutual coupling).

I seriously have doubts on this mutual coupling or double cone area = 3dB
You surely have benefits from mutual coupling, like lower frequency cutoff, but not in SPL. I would have to find the article about air impedance and pressure to re-examine it.

It would be too easy anyways, just put a gazillion of speakers an you can do a 10 000 people venue with 100W... :blink:

JBL 4645
02-02-2011, 09:54 AM
Not gonna read that because it hurts my eyes,

Buggers my eyes in as well! That's a hush background :blink: colour. I was going to copy paste but...20000 characters long! I can't read it not without having a headache.

Try highlighting the page with mouse so the screen goes blue with white text, its less hush on the eye, over the turquoise.

pos
02-02-2011, 01:02 PM
The situation is quite simple:
when doubling the amplitude of a signal you get a 6dB gain.
To achieve this acoustically you need to double the volume of air that is moved.

For one speaker that means doubling the excursion, which requires to double the tension, which implies multiplying the power by four (P = U^2/R, ).
You can also achieve the same result by keeping the excursion constant and doubling the cone area (still twice the volume of air moved) OR doubling the number of cones of same area (and feeding each cone with the same power).

of course running one amplifier with half the impedance load is a way to acheive a (near) doubling of the power, but lets say for the sake of simplicity that we use two amps instead of one, with the same power for each.

So with two speakers you double your power (same power for each speaker) but you get a 6dB boost. BUT there is a catch: you only get that boost where the signal from the two cones sum in phase. That means on a straight line between the two cones for all frequencies, and also around that line for the lower frequencies (the lower you go, the further around the line you get the inphase summation). This is a basic directivity phenomenone, similar to what you get with a single one, but of course with two cones it strikes lower in frequency...
Where the summation is not in phase (farther from the line and higher in frequency) you only get a 3dB boost (quadratic summation).

Of course in a real room the situation is more complicated, but the reasoning is the same. This is only the places where you get that in phase summation (not a straigth line anymore...) that are more complicated to predict.

Eaulive
02-02-2011, 04:27 PM
The situation is quite simple:
when doubling the amplitude of a signal you get a 6dB gain.
To achieve this acoustically you need to double the volume of air that is moved.

For one speaker that means doubling the excursion, which requires to double the tension, which implies multiplying the power by four (P = U^2/R, ).
You can also achieve the same result by keeping the excursion constant and doubling the cone area (still twice the volume of air moved) OR doubling the number of cones of same area (and feeding each cone with the same power).

of course running one amplifier with half the impedance load is a way to acheive a (near) doubling of the power, but lets say for the sake of simplicity that we use two amps instead of one, with the same power for each.

So with two speakers you double your power (same power for each speaker) but you get a 6dB boost. BUT there is a catch: you only get that boost where the signal from the two cones sum in phase. That means on a straight line between the two cones for all frequencies, and also around that line for the lower frequencies (the lower you go, the further around the line you get the inphase summation). This is a basic directivity phenomenone, similar to what you get with a single one, but of course with two cones it strikes lower in frequency...
Where the summation is not in phase (farther from the line and higher in frequency) you only get a 3dB boost (quadratic summation).

Of course in a real room the situation is more complicated, but the reasoning is the same. This is only the places where you get that in phase summation (not a straigth line anymore...) that are more complicated to predict.

Doubling the volume of air that is moved.... yes but no, a speaker is less than a perfectly efficient device, if you double the cone area, you also double the weight of the cone, then you have compliance issues and other considerations as well. This is all theoretical.

According to this statement this means that a 15" with the same type of cone and motor than a 12" would have 3.9dB gain over the 12" since it's 1.6 times bigger. Try the many JBL woofers that share the same motor just for fun.
The 2226 / 2206 comparison is 2dB sensitivity and the 2241 has 3dB over the 2206 while having 2.25 times the surface.

If it was that easy to achieve 6dB gain when doubling the cone area, there would be very big woofers around. :)

As for doubling the number of drivers, since they can not be in the same point source, there will be delays, you might get 6dB at some frequencies when in line, but only if the two sources have created a null on their sides.
I.E: with two speakers spaced by 1/2 wavelength, there is a theoretical cancellation at 90 and 270 degrees from the plane, in this case there will be a 3dB gain at 0 and 180 degrees. Energy is not created, it is merely beamed.

So yes, in theory that 3dB gain compounded with the 3dB gain from the power being double will yield a 6dB increase, but it's highly frequency dependent.

We use that system in SR with _multiple_ subwoofers to steer the energy in a given direction.

HCSGuy
02-02-2011, 08:34 PM
The original question was do you get mutual coupling in a room with multiple subwoofers, which I think it is agreed you do not unless they activate all room modes equally, which requires they be in the same location. If they are not located together, the resultant frequency response is highly variable from seat to seat. Lucky for us, our friends at Harman unleashed a little of their energy and lab time and explored the use of multiple subwoofers in an enclosed room, modeling up to 5000 subs in one room, and measuring up to (I think) 18. Here is a brief, very readable pdf of a power point on the subject by Todd Welti - skip to the end first and see their findings, then work back to see how they got there:

http://www.harman.com/EN-US/OurCompany/Technologyleadership/Documents/White%20Papers/multsubs.pdf

I understand Dr. Floyd Toole also participated in this research, and it is mentioned in his book on sound reproduction - it's a great practical addition to F Alton Everest's Master Handbook of Acoustics, though I personally find Everest's an easier read...

http://www.amazon.com/Sound-Reproduction-Acoustics-Psychoacoustics-Loudspeakers/dp/0240520092/ref=sr_1_1?ie=UTF8&s=books&qid=1296707309&sr=8-1

Maybe they'll release a book-on-CD version of it, maybe with Sir Ian McKellen reading :p

Summary, if you've got two subwoofers, put them in the front and back of the room, centered on the walls.

pos
02-03-2011, 12:43 AM
Eaulive, I think we agree

If a doubling in the volume of air moved is achieved, 6dB is gained, after that it is all down to how to obtain this doubling of air moved.

At low enough a frequency and with close enough drivers (OR if you are exactly on a line between these drivers, what we could call "on axis" of the couple of drivers), two drivers will sum in phase.
In this precise situation, if you feed each driver with 100W you obtain the same SPL than if you fed only one driver with 400W, that is +6dB.
Then the cancellation lobes and quadratic summation that you can get at higher frequencies and/or when the drivers a farther apart and when you move off axis is a pure directivity issue, exactly the same issue a what you get with a single driver when the frequency is raised (think about a polar plot).

The "mutual coupling" rule is simply a case where when the frequency is low enough and the drivers are close enough, you get a reasonable in phase summation at a reasonably large angle around the axis, and effectively get this 6dB boost.

Allanvh5150
02-07-2011, 10:42 PM
To much thinking going on. This is sub bass people. 3db 6db, I am sure we can measure that in the lab but in our houses there are many things that come into play. Plain and simple, Subs are power hungry and need to be driven with an oversize amplifier as to remain in control of the cone excursion. My HT room is 7m x 5m and it has 2 pair of 2235's. Two at the front an two at the rear. Each pair is driven with 1000 watts. I have not even measured the level of the subs but I can tell you that if they are run at full power they will probably start loosening the fittings in the house. I have never had an issue with subs even though they are driven with more than triple thier RMS power. I think the problems begin when subs are underpowered and the amplifier can't control the cone properly. Do no think about making your amplifiers smaller even though when calculated, you should be able to do so.

Allan.