# Dual Opposed Subwoofer Theory?

#### digitalfrost

##### Major Contributor
Forum Donor
This is not mine, I found it somewhere, but it could explain what you were seeing with regards to isobaric:

By electrically and acoustically coupling two woofers (coupled-chamber or compound principle), the required cabinet volume can be reduced by about half of what would be required if only one chassis were used.
Compound systems, however, are basically no different in construction than single-chassis systems. The calculation of cabinet sizes, tuning tunnels etc. is completely identical, only the (modified) TSP of the compound chassis has to be used. The acoustic (airtight) coupling and electrical interconnection of two (usually identical) chassis creates a new chassis with new TSP. If the coupling volume is practically 0 ltr. the TSP of the new compound chassis are also practically identical with the exception of the Vas, Re, Le and the efficiency.

The Vas is halved, since per chassis only "one side" of the diaphragm contributes to the acoustic power respectively the diaphragm mass is at least doubled. Therefore, the efficiency also decreases by half, SPL decreases by 3 dB. Re and Le change in dependence on the electrical connection, with parallel connection Re and Le are halved with series connection doubled.

In practice, the coupling volume is neither 0 ltr. nor 100% tight. Therefore, all TSP change more or less strongly compared to the single chassis. The air of the coupling volume has a mass of approx. 1.18 g/l which is added to the moving mass of the two single chassis. Due to the more than double mass compared to the single chassis, the resonant frequency fo decreases and Qm, Qe and thus Qt change. Since the decrease of the resonant frequency is square root proportional to the increase of the mass, the Vas of the compound chassis decreases even with a coupling volume of more than 0 lt. also only by half of the Vas of a single chassis. However, due to the increased mass, the efficiency drops by more than 3dB compared to the single chassis.

K ~ correction factor due to chamber volume in Ltr.
Vas'=Vas/2
K = (2* mass + coupling volume* 1.18 g) / 2 / mass
fo' = fo / (K ^ 0.5)
Qm' = Qm / (K ^ 0.5)
Qe' = Qe * (K ^ 0.5)
Qt' = (Qm' * Qe') / (Qm' + Qe')
N%' = 0.000000000964 * fo' ^ 3 * Vas' / Qe'
SPL' = 112 + 10 * (Log(N%') / Log(10))

e: Added some more explanation.

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#### audiofooled

##### Senior Member
That has not been my experience.

Back in the early 80's I built several homebrew isobaric subwoofers. To my ears they seemed to outperform what the math predicted. I borrowed some test equipment from the college I was attending and made some close-miked frequency response measurements, comparing a sub with two woofers in a sealed isobaric configuration in one cubic foot total internal volume, versus a single woofer (same woofer, a large Dynaudio) in a two cubic foot sealed box. My measurements seemed to confirm what my ears were saying, the isobaric enclosure behaved as if it had a higher system Q and it went deeper.

I don't claim to have an explanation for my observations, but I speculate that the published math for isobaric woofer systems fails to take into account the addition of at least some of the airmass in the isochamber to the moving mass of the cones.

Low frequency extension is a close call between the two, matter of couple of Hz and a single db, if any. But doubling or halfing the box size may not behave in a linear fashion for any box size, or any parameters of the driver. 1 or even 2 cubic feet is still a small box so it might have been that isobaric worked better in your case. Question would be how do you level match to compare since the power handling, also excursion is very different? At higher spl, an isobaric pair may still not have reached xmax, except at single digit frequencies. If you have enough power at hand, isobaric can beat single driver, even though inefficient as it is. Modern software certainly takes into account added mass, even losses if you will, but it cannot predict 100%.

#### dfuller

##### Major Contributor
Barefoot explains it rather well here:
TL;DW version, the drivers operate equal but opposite. They're within 1/4 wavelength throughout their passband so they act as effectively one driver but cancel the force acting on the cabinet so resonances are essentially nonexistent.

#### Duke

##### Major Contributor
Audio Company
Forum Donor
Low frequency extension is a close call between the two, matter of couple of Hz and a single db, if any. But doubling or halfing the box size may not behave in a linear fashion for any box size, or any parameters of the driver. 1 or even 2 cubic feet is still a small box so it might have been that isobaric worked better in your case.

Close-miked, the two cubic foot sealed enclosure was -3 dB in the low 70's, below which the measured initial rolloff was fairly gradual (approximately 9 dB per octave as I recall). The math predicted a low Qtc sealed box, and the measured frequency response agreed with that.

Close-miked, the one cubic foot sealed isobaric enclosure was -3 dB in the upper 40's, below which the measured initial rolloff was noticeably steeper (approximately 15 dB per octave as I recall). This was of course very different from what was predicted by the math I had access to at the time (1984).

The woofers were 8" Dynaudio units, the 21W54.

I speculate that the relatively low moving mass of the Dynaudio woofers (I don't recall their moving mass but they were not designed specifically for subwoofer duties) made their parameters particularly sensitive to the additional moving mass contributed by coupling to the air in the isochamber. [Edit - I now think the air mass in the isochamber, about 12 grams, was not enough to explain the measured difference even if coupling efficiency was 100%).

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#### audiofooled

##### Senior Member
Close-miked, the two cubic foot sealed enclosure was -3 dB in the low 70's, below which the measured initial rolloff was fairly gradual (approximately 9 dB per octave as I recall). The math predicted a low Qtc sealed box, and the measured frequency response agreed with that.

Close-miked, the one cubic foot sealed isobaric enclosure was -3 dB in the upper 40's, below which the measured initial rolloff was noticeably steeper (approximately 15 dB per octave as I recall). This was of course very different from what was predicted by the math I had access to at the time (1984).

The woofers were 8" Dynaudio units, the 21W54.

I speculate that the relatively low moving mass of the Dynaudio woofers (I don't recall their moving mass but they were not designed specifically for subwoofer duties) made their parameters particularly sensitive to the additional moving mass contributed by coupling to the air in the isochamber.

Ok, this is quite big of a box then, about twice as big in either case (I thought drivers were bigger). I tried couple of plots in WinISD with some T/S parameters I could find for this driver. It really shows identical transfer function magnitude in both cases, until you start to manually enter added mass to the cone. Basically, to make an F3 of 50 Hz, added mass should be 30g (about 1 oz), so more than that for the upper 40's, which is roughly a moving mass of another cone.
Interestingly enough, when adding mass to the isobaric one, it does show raised Qtc (0,576 as opposed to 0,475), so better damping, but an even more gradual rolloff (contrary to your observation). When I try an SPL plot, it shows worse excursion limits for isobaric (it will go over xmax below 28 Hz for double the power, while for the same excursion single one would beat it in spl by far for any frequency above 28 Hz).
Basically, WinISD would recommend two of the drivers in normal alignment so that both pump the same chamber in the 1 cu.ft enlosure. This would read a Qtc of 0.720 (fairly close to magical 0.707 for flat amplitude response). This is predicted to be most efficient but it would be just a woofer, rather than subwoofer, which leads us to your remark about the actual driver properties with regards to application. Anyway, this is all with room not included in the equation.
My conclusion with this kind of software is that it favors larger cone area (or a lot of excursion) for any useful output below 40 Hz (or even 50) and actual driver parameters adequate for subwoofer application. Trying to turn a woofer into a subwoofer can lead to funny results (either double the excursion limits) or ridiculous added masses which beats the purpose of one another.
However, if you allow me, I may just try and speculate how you succeeded with isobaric one. It did go lower when, as @digitalfrost posted, some mass is added into the equation (beats me how much), and power handling (more than double) would allow it to play over 30 Hz and be in the excursion safe zone. The only question would be did it quickly bottom out bellow 30, as predicted by the software...
Other than that, have you tried to compare the two in a room (I suppose you haven't completed two of them, but rather one by one, because it would take 3 drivers)? Was there an audible difference in THD or SQ? How 'bout SPL? Enclosure stiffness (bracing), stuffing, etc? Amp?

#### egellings

##### Major Contributor
Compared to the moving mass of the two drivers, is the mass of the air trapped between them significant?

#### Chrise36

##### Addicted to Fun and Learning
Ok, this is quite big of a box then, about twice as big in either case (I thought drivers were bigger). I tried couple of plots in WinISD with some T/S parameters I could find for this driver. It really shows identical transfer function magnitude in both cases, until you start to manually enter added mass to the cone. Basically, to make an F3 of 50 Hz, added mass should be 30g (about 1 oz), so more than that for the upper 40's, which is roughly a moving mass of another cone.
Interestingly enough, when adding mass to the isobaric one, it does show raised Qtc (0,576 as opposed to 0,475), so better damping, but an even more gradual rolloff (contrary to your observation). When I try an SPL plot, it shows worse excursion limits for isobaric (it will go over xmax below 28 Hz for double the power, while for the same excursion single one would beat it in spl by far for any frequency above 28 Hz).
Basically, WinISD would recommend two of the drivers in normal alignment so that both pump the same chamber in the 1 cu.ft enlosure. This would read a Qtc of 0.720 (fairly close to magical 0.707 for flat amplitude response). This is predicted to be most efficient but it would be just a woofer, rather than subwoofer, which leads us to your remark about the actual driver properties with regards to application. Anyway, this is all with room not included in the equation.
My conclusion with this kind of software is that it favors larger cone area (or a lot of excursion) for any useful output below 40 Hz (or even 50) and actual driver parameters adequate for subwoofer application. Trying to turn a woofer into a subwoofer can lead to funny results (either double the excursion limits) or ridiculous added masses which beats the purpose of one another.
However, if you allow me, I may just try and speculate how you succeeded with isobaric one. It did go lower when, as @digitalfrost posted, some mass is added into the equation (beats me how much), and power handling (more than double) would allow it to play over 30 Hz and be in the excursion safe zone. The only question would be did it quickly bottom out bellow 30, as predicted by the software...
Other than that, have you tried to compare the two in a room (I suppose you haven't completed two of them, but rather one by one, because it would take 3 drivers)? Was there an audible difference in THD or SQ? How 'bout SPL? Enclosure stiffness (bracing), stuffing, etc? Amp?
If you tune it right a bandpass can have significant spl increase in a narrow frequency range and the room will amplifiy that so in some applications you get significant boost in moderate sized boxes. If it is a 4th order bandpass the group delay is kept in control also.

#### Duke

##### Major Contributor
Audio Company
Forum Donor
Other than that, have you tried to compare the two in a room (I suppose you haven't completed two of them, but rather one by one, because it would take 3 drivers)? Was there an audible difference in THD or SQ? How 'bout SPL? Enclosure stiffness (bracing), stuffing, etc? Amp?

The application was in an active two-way system with two Strathearn "ribbons" (actually planar magnetics) per side, atop the Dynaudio woofer boxes. I don't recall the crossover frequency but probably in the 200 Hz ballpark.

The audible difference was in the tonal balance.

The one cubic foot isobaric enclosure was made of 3/4" veneered MDF, and the two cubic foot sealed box was made of double-thicked 3/4" MDF, so 1.5" thick, with one internal brace. I don't remember the details of the stuffing material and density, but it would have been similar.

This was 37 years ago, but I remember the results well because they were not anticipated. I had been using the sealed boxes and then tried the isobaric to save space. The audible difference surprised me so I borrowed measuring equipment from the college I was attending.

The Dynaudio woofers did not audibly distort in that application. The outer woofer may well have exceeded its linear excursion at times but I don't recall ever hearing it distort, and I used that system for almost two years (which was a record for me, at the time). On the other hand I had previously built an isobaric subwoofer using the KEF B139 and it could get a bit tubby when pushed hard. I transferred the B139s to a smaller isobaric enclosure and that actually worked better because I could turn it up louder without audible distortion.

Compared to the moving mass of the two drivers, is the mass of the air trapped between them significant?

Excellent question! I'd never actually calculated it, and now that I have, it does not seem to be very significant: Assuming 1/3 of a cubic foot of air in the isochamber, the mass would be about 12 grams.

So the trapped airmass idea no longer seems like a plausible explanation to me.

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#### Chrise36

##### Addicted to Fun and Learning
The application was in an active two-way system with two Strathearn "ribbons" (actually planar magnetics) per side, atop the Dynaudio woofer boxes. I don't recall the crossover frequency but probably in the 200 Hz ballpark.

The audible difference was in the tonal balance.

The one cubic foot isobaric enclosure was made of 3/4" veneered MDF, and the two cubic foot sealed box was made of double-thicked 3/4" MDF, so 1.5" thick, with one internal brace. I don't remember the details of the stuffing material and density, but it would have been similar.

This was 37 years ago, but I remember the results well because they were not anticipated. I had been using the sealed boxes and then tried the isobaric to save space. The audible difference surprised me so I borrowed measuring equipment from the college I was attending.

Excellent question! I'd never actually calculated it, and now that I have, it does not seem to be very significant: Assuming 1/3 of a cubic foot of air in the isochamber, the mass would be about 12 grams.

So the trapped airmass idea no longer seems like a plausible explanation to me.
The push pull action also may have an effect in suspension compliance bringing fs further down.

#### Wes

##### Major Contributor
Forum Donor
• They take less floor space than two separate subs
• They usually cost less than two separate subs
• Yet they provide the power of two subs
• They don't vibrate themselves or the floor much (could be a pro or con)

yet they don't resolve the nodes in the room issues like two separate subs do...

#### digitalfrost

##### Major Contributor
Forum Donor
That's why you use multiple dual opposed subs.

#### Duke

##### Major Contributor
Audio Company
Forum Donor
yet they don't resolve the nodes in the room issues like two separate subs do...

Agreed.

Contrary to popular opinion, EQ of a single high-quality sub is not the solution seems to be at first glance. EQ cannot fix a cancellation dip, but spreading multiple bass sources intelligently around the room can. And THEN if you want to add EQ, its effectiveness isn't limited by cancellation dips.

#### audiofooled

##### Senior Member
The push pull action also may have an effect in suspension compliance bringing fs further down.

Yes, the software takes this into account, Double Mms, half the Cms, half the Vas, half the box, and it predicts exactly the same FR for both situations. This guy tested this:

So, confirmed (note that the air mass in the iso chamber can do something to lower the Fs, but not much). Basically, the only benefit should be smaller box. But in this case, both of the box sizes are suitable for the driver, also the driver is suitable for subwoofer application.

@Duke saw benefits besides that, and I believe that he did, and that's why I'm intrigued what's the physics behind this.

#### audiofooled

##### Senior Member
The application was in an active two-way system with two Strathearn "ribbons" (actually planar magnetics) per side, atop the Dynaudio woofer boxes. I don't recall the crossover frequency but probably in the 200 Hz ballpark.

The audible difference was in the tonal balance.

The one cubic foot isobaric enclosure was made of 3/4" veneered MDF, and the two cubic foot sealed box was made of double-thicked 3/4" MDF, so 1.5" thick, with one internal brace. I don't remember the details of the stuffing material and density, but it would have been similar.

This was 37 years ago, but I remember the results well because they were not anticipated. I had been using the sealed boxes and then tried the isobaric to save space. The audible difference surprised me so I borrowed measuring equipment from the college I was attending.

The Dynaudio woofers did not audibly distort in that application. The outer woofer may well have exceeded its linear excursion at times but I don't recall ever hearing it distort, and I used that system for almost two years (which was a record for me, at the time). On the other hand I had previously built an isobaric subwoofer using the KEF B139 and it could get a bit tubby when pushed hard. I transferred the B139s to a smaller isobaric enclosure and that actually worked better because I could turn it up louder without audible distortion.

Excellent question! I'd never actually calculated it, and now that I have, it does not seem to be very significant: Assuming 1/3 of a cubic foot of air in the isochamber, the mass would be about 12 grams.

So the trapped airmass idea no longer seems like a plausible explanation to me.

Those drivers were good. Low Mms and a good Bl possibly aided low distortion. Maybe even cranking them in free air would't break them. With such a low Qts in too big of a box they did something maybe counter intuitive. They didn't bump the FR in higher bass frequencies and neither did they distort in lower.
To me this is quite interesting. My towers have featherweight 5" drivers and they act as if they don't need any damping at all. In a large ported enclosure they play so low that to this day it never ceases to amaze me. What they lack is a bit punch up higher (they are small to couple enough air for this), and this is where a 12 inch sealed sub in a 2,6 cu.ft enclosure comes to aid. In room, to me, this proved to be one hell of a combination.

#### Oztayls

##### Member
This has been a fascinating discussion to read. I’m currently in the process of building a pair of open baffle subs. The plan is to power each of them with their own plate amp. The drivers are 15” W15s from Lii Audio, really heavy suckers which have twin 8ohm voice coils that can be wired in parallel or series.

When searching for suitable plate amps, I came across one that can run a pair of drivers in opposite phases. It seems to me that the amp is really a pair of amps that drives the phases separately. Would this type of amp be suitable for a twin coil driver do you think?

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#### Don Hills

##### Addicted to Fun and Learning
That amp is less than optimal for a driver with twin 8 ohm voice coils. You'll get only half its rated power output. You could likely drive both of your drivers from one amp. Wire each driver's voice coils in series to give a 16 ohm load each, then wire the drivers in parallel to provide a total load of 8 ohms.

#### Oztayls

##### Member
That amp is less than optimal for a driver with twin 8 ohm voice coils. You'll get only half its rated power output. You could likely drive both of your drivers from one amp. Wire each driver's voice coils in series to give a 16 ohm load each, then wire the drivers in parallel to provide a total load of 8 ohms.
Thanks, I wasn't sure how these things worked. The amp is rated 280W, so I was figuring half of that for each phase giving full power for both. I might just look for something conventional that I know works. I've tested the driver with a 300W Class D plate amp, and it works well, plenty of grunt. I think I'd prefer a Class AB though.

#### NiagaraPete

##### Major Contributor
Forum Donor
The best two examples are the Kef kc62 and svs micro 3000.

#### Chromatischism

##### Major Contributor
Forum Donor
The best two examples are the Kef kc62 and svs micro 3000.
For dual opposed? Disagree. Rythmik and PSA are way, way better.

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