# Simulation Overview of the 'Double Bass Array' Configuration.

#### René - Acculution.com

##### Senior Member
Technical Expert
I will give a short introduction via simulations in COMSOL Multiphysics to the ‘Double Array Bass’ subwoofer setup and how the response will differ between an idealized situation of two walls moving compared to having a finite number of subwoofers.

Imagine first a 3x4x5 meters room. We can calculate the associated room modes as shown below.

These modes are an inherent feature of the room geometry and air being the medium inside it. They exist independent of any sources and are calculated without any regard to sourcing. Whether a mode is a problem or not will be evaluated when a source(s) is activated. Let us now put a subwoofer in the corner and evaluate the sound pressure level in 6 preselected places at a height of 1.1 meters.

The responses in the points vary quite a bit.

Some distinct issues can be seen at frequencies where there is a mode, but it would be wrong to say that a mode will always cause a resonance; that will depend on the source type and characteristics, and placement of both source(s) and your ears.

Many different multi-sub approaches could now be tried out but let us focus on the so-called Double Bass Array method. Here, the strategy basically is to turn the room into a tube. Tube acoustics is a little more involved than room acoustics (and a good topic if you want to really understand room acoustics better), but there is one major thing to understand: “The plane wave will always propagate”. Tube modes differ from room modes in that the former type really exist at all frequencies at once and will either propagate if excited above an associated modal frequency or die out as an evanescent wave below it. The only wave that will always propagate is the plane wave, and one way to achieve a propagating plane wave is to excite both the front wall and the rear wall in a pistonic-like fashion as shown in the animation below.

The front wall has its particular displacement, and the rear wall has a modified displacement to account for the phase shift coming from the wave travelling the room distance. You now effectively sit in an infinite tube with only a travelling wave and no reflection. Let us look at the response for this case.

We have a one-dimensional sound field, with a travelling wave and no reflection. If the excitation is the entirety of the walls in a pistonic matter, this will be the case at all frequencies(!), no matter how high.

Now comes the practical implementation. With 4 subwoofers at the front wall, and 4 subwoofers at the rear wall with a phase modification to their response, a placement can be found that tries to emulate the full wall moving. Each driver sits 1/4 of the width/hight of the room away from the wall and are spaced 1/2 of that apart to have the mirror sources be spaced equally. We assume that the subwoofers are very flat or placed in the wall somehow as shown below.

The corresponding responses actually look very good still at the low frequencies we are considering here.

With the simulation setup in place, you can now experiment away and for example investigate what happens if the four upper subwoofers are not connected.

You could argue that they should be placed halfway up now, but I am going with this setup, since you probably have to place them near the floor in most situations anyway. In general, as you stray more and more away from the ‘walls moving’ situation, the response curves will naturally take a hit.

One can consider dropping the subwoofers at the rear wall and replace them with damping material. To investigate via simulations you will have to have some idea of that setup with damping material parameter and such.

You will need more than a phase knob
on your subwoofers to do this, as there is a time delay involved and that will not give you one phase for all frequencies, so some kind of DSP is needed.

Hopefully you have gotten the idea behind the DBA principle, and of course ask questions if something is not clear.

René Christensen, Denmark, BSEE, MSc (Physics), PhD (Microacoustics), FEM and BEM simulations specialist in/for loudspeaker, hearing aid, and consultancy companies. Own company Acculution, blog at acculution.com/blog

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#### Cbdb2

##### Major Contributor
The subs on the second wall are supposed to "remove that wall" so theres no reflection? So there active absorbers similar to an out of phase woofer right beside an in phase one? Why are there no modes in the other 2 directions? What happens in a real room with walls that have a good amount of frequency dependent low end absorption? And I guess this removes all the room gain.

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OP

#### René - Acculution.com

##### Senior Member
Technical Expert
The subs on the second wall are supposed to "remove that wall" so theres no reflection? So there active absorbers similar to an out of phase woofer right beside an in phase one? Why are there no modes in the other 2 directions? What happens in a real room with walls that have frequency dependent low end absorption?
Yes they effectively works as an absorbing layer. The rear wall has a specialised displacement that follows the displacement that the travelling wave has and would have were the room infinitely long. But an out of phase sub next to one of the subs will be a very different situation where you create a dipole. The point of the DBA is to create the travelling wave in a confined space.

The wave only travels in one direction and so no modes are excited in the idealised tube situation. Looking at higher frequencies you will see that a finite number of subs will not be enough and modal behaviour will become more important, but you will be crossing over to your mains anyway.

I would need to know what the absorption is. I can try and put a thick layer of foam but then more and more thinks could be tried out.

#### JPA

##### Active Member
Forum Donor
Good post. I'm very interested in DBA because I currently have a house under construction that will have a dedicated home theater room. I'm planning to experiment with both Welti multi-sub configurations and DBA. I'll report on my observations and measurements when the room is ready, but that's several months down the road.

The main problem with DBA aside from the cost of the multiple subs is that efficiency is low. You pay the full cost of the rear subs and amplification, but they don't contribute to the bass SPL at the listening positions. I was wondering the other day how a "hybrid" or "part-time" DBA implementation would sound. In this scheme, you would use the rear subs only to cancel the room modes, and let the other frequencies go uncancelled. You'd set it up by measuring the frequency response at the rear wall, identify the modes, then use a parametric equalizer to create a peak for each mode at the rear subs. That would cause them activate and cancel only the modes, and leave the other frequencies alone.

Can that be simulated in COMSOL Multiphysics?

#### voodooless

##### Grand Contributor
Forum Donor
Cool sims. I’ve looked up some previous threads on this, notably one from @ppataki. Interesting was post 2:

Specifically this image:

Now in that case the rear sub was delayed about 16ms. So here it looks like the rear delayed wave still reaches the listener. It is about 10 dB less loud though. So what gives?

So here is my gut reaction: by the time the front wave gets to the rear, it’s attenuated (inverse square law). Now if the rear sub plays at the same volume as the front, it will not just cancel out the front, but will still send energy back. So to really cancel out, you’ll need to attenuate the rear sub as much as the front sub looses over the distance. Am I right in this?

Sadly, I have an L-shaped room . It would require a shitload of drivers, and multiple delays to get that working.

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OP

#### René - Acculution.com

##### Senior Member
Technical Expert
Good post. I'm very interested in DBA because I currently have a house under construction that will have a dedicated home theater room. I'm planning to experiment with both Welti multi-sub configurations and DBA. I'll report on my observations and measurements when the room is ready, but that's several months down the road.

The main problem with DBA aside from the cost of the multiple subs is that efficiency is low. You pay the full cost of the rear subs and amplification, but they don't contribute to the bass SPL at the listening positions. I was wondering the other day how a "hybrid" or "part-time" DBA implementation would sound. In this scheme, you would use the rear subs only to cancel the room modes, and let the other frequencies go uncancelled. You'd set it up by measuring the frequency response at the rear wall, identify the modes, then use a parametric equalizer to create a peak for each mode at the rear subs. That would cause them activate and cancel only the modes, and leave the other frequencies alone.

Can that be simulated in COMSOL Multiphysics?
It is a crazy concept when it comes to implementation, so it would be very interesting to follow your work.

Well you can simulate most things in Comsol Multiphysics. One could consider letting Comsol do the optimisation of placement, level and phase based on certain objectives.

OP

#### René - Acculution.com

##### Senior Member
Technical Expert
Cool sims. I’ve looked up some previous threads on this, notably one from @ppataki. Interesting was post me 2:

Specifically this image:

View attachment 234727

Now in that case the rear sub was delayed about 16ms. So here it looks like the rear delayed wave still reaches the listener. It is about 10 dB less loud though. So what gives?

So here is my gut reaction: by the time the front wave gets to the rear, it’s attenuated (inverse square law). Now if the rear sub plays at the same volume as the front, it will not just cancel out the front, but will still send energy back. So to really cancel out, you’ll need to attenuate the rear sub as much as the front sub looses over the distance. Am I right in this?

Sadly, I have an L-shaped room . It would require a shitload of drivers, and multiple delays to get that working.
There are no losses in the simulated room here, but a real room would have losses that take out energy of the wave. Perfect transmission can probably not be expected in real life. Also, the subs need to sit flush on the wall for this idealised case.

#### ppataki

##### Major Contributor
Cool sims. I’ve looked up some previous threads on this, notably one from @ppataki. Interesting was post 2:

Specifically this image:

View attachment 234727

Now in that case the rear sub was delayed about 16ms. So here it looks like the rear delayed wave still reaches the listener. It is about 10 dB less loud though. So what gives?

So here is my gut reaction: by the time the front wave gets to the rear, it’s attenuated (inverse square law). Now if the rear sub plays at the same volume as the front, it will not just cancel out the front, but will still send energy back. So to really cancel out, you’ll need to attenuate the rear sub as much as the front sub looses over the distance. Am I right in this?

Sadly, I have an L-shaped room . It would require a shitload of drivers, and multiple delays to get that working.

@voodooless In my case this experiment was kind of a failure since I have an odd shaped room (6 corners instead of 4....) and I tried it with 2 subs only
I read somewhere that the rear subs shall have the same volume as the fronts
But I guess this is all down to experimentation at the end of the day....
In my current room I would not try this again but in a regular shaped room definitely! (with at least 4 subs)

#### Flaesh

##### Senior Member
I just saw this thread .
BTW, I registered here mainly in the hope of talking about DBA, but here, as well as on local forums and diyaudiocom, almost no one builds and only doubt the usefulness of the idea.

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#### Flaesh

##### Senior Member
I was wondering the other day how a "hybrid" or "part-time" DBA implementation would sound. In this scheme, you would use the rear subs only to cancel the room modes, and let the other frequencies go uncancelled.
It seems wrong.
The goal is a travelling plane wave and no reflection.

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#### Flaesh

##### Senior Member
I read somewhere that the rear subs shall have the same volume as the fronts
In real room rear subs shall have slightly less volume and same [as possible] FR and PhR as the fronts. Simple IIR eq may help if different subs used.

OP

#### René - Acculution.com

##### Senior Member
Technical Expert
It seems wrong.
The goal is a travelling plane wave and no reflection.
And the room modes can never be 'cancelled'. They always exist, regardless of source setup. The question is to what degree the modes are excited by the sources.

#### JPA

##### Active Member
Forum Donor
It seems wrong.
The goal is a travelling plane wave and no reflection.
Well, I have two goals. The first is to eliminate or greatly reduce room modes. The second is to achieve a high ratio of dinosaur stomp volume to subwoofer count.

Besides, I'm concerned about how effective DBA is in a real HT with tiered seating and human bodies to disrupt that nice laminar flow of bass waves.

#### Flaesh

##### Senior Member
how effective DBA is
Very effective in cuboidal room . Have you room plan\drawing\pics? Asymmetric openings in fron and rear walls are the worst. And what upper frequency for subs do you need?
SBA can be an alternative. Nils Öllerer aka FoLlGoTt used both in his HT.
"Source to sink" (in Fazenda's terms) systems with subs on floor aren't DBA, while subjectively may be rated good; I haven't opportunity to listen SS.

OP

#### René - Acculution.com

##### Senior Member
Technical Expert
Very effective in cuboidal room . Have you room plan\drawing\pics? Asymmetric openings in fron and rear walls are the worst. And what upper frequency for subs do you need?
SBA can be an alternative. Nils Öllerer aka FoLlGoTt used both in his HT.
"Source to sink" (in Fazenda's terms) systems with subs on floor aren't DBA, while subjectively may be rated good; I haven't opportunity to listen SS.
I can set up an optimisation routine in Consol that will find the best subwoofer settings for a quasi plane wave for a given room.

#### andyc56

##### Active Member
I will give a short introduction via simulations in COMSOL Multiphysics to the ‘Double Array Bass’ subwoofer setup and how the response will differ between an idealized situation of two walls moving compared to having a finite number of subwoofers.

[...]

Hopefully you have gotten the idea behind the DBA principle, and of course ask questions if something is not clear.

I have a question. In Beranek's original book from the '50s, there is an equation (4.17) for the acoustic pressure at a point at a given distance from a rigid piston in an infinite baffle under anechoic conditions. That pressure is proportional to j * omega * u, where u is the velocity amplitude of the piston's (assumed sinusoidal) motion. In the time domain, this of course translates to the time derivative of the piston's velocity (that is, its acceleration). So for a constant acoustic pressure vs. frequency, the acceleration amplitude of the piston must be constant with frequency as well. Of course, this is the same as saying the displacement amplitude must be inversely proportional to the square of the frequency for a constant acoustic pressure vs. frequency at a fixed distance and location (since acceleration must be integrated with respect to time twice to get displacement). So in the case of radiation from a piston in an infinite baffle, for the same acoustic pressure at half of some reference frequency, the piston's displacement amplitude must be 4 times its value at the reference frequency.

Your plot of the SPL response of the ideal DBA shows a curious downward slope vs. frequency, maybe -6 dB/octave or so? So my question is this: what is the assumed displacement amplitude vs. frequency of the "pulsating wall" in this simulation? Is it chosen to give a constant acceleration amplitude vs. frequency (that which would give a flat anechoic response in the "radiation from a piston" case)?

Thanks.

OP

#### René - Acculution.com

##### Senior Member
Technical Expert
I have a question. In Beranek's original book from the '50s, there is an equation (4.17) for the acoustic pressure at a point at a given distance from a rigid piston in an infinite baffle under anechoic conditions. That pressure is proportional to j * omega * u, where u is the velocity amplitude of the piston's (assumed sinusoidal) motion. In the time domain, this of course translates to the time derivative of the piston's velocity (that is, its acceleration). So for a constant acoustic pressure vs. frequency, the acceleration amplitude of the piston must be constant with frequency as well. Of course, this is the same as saying the displacement amplitude must be inversely proportional to the square of the frequency for a constant acoustic pressure vs. frequency at a fixed distance and location (since acceleration must be integrated with respect to time twice to get displacement). So in the case of radiation from a piston in an infinite baffle, for the same acoustic pressure at half of some reference frequency, the piston's displacement amplitude must be 4 times its value at the reference frequency.

Your plot of the SPL response of the ideal DBA shows a curious downward slope vs. frequency, maybe -6 dB/octave or so? So my question is this: what is the assumed displacement amplitude vs. frequency of the "pulsating wall" in this simulation? Is it chosen to give a constant acceleration amplitude vs. frequency (that which would give a flat anechoic response in the "radiation from a piston" case)?

Thanks.
I am in the process of moving so I will get back to this later. The sound field to look up is the that of a tube, not an infinite baffle.

#### Flaesh

##### Senior Member
under anechoic conditions.
*BA (DBA or SBA) radiate in (approx.) PWT, plane wave tube. So anechoic spherical radiation equations are not veri useful for this. The simplest and accessible for all Hornresp can give you an idea if you consider infinite horn. Subs may be as low Q as available.

Funny intermediate case is linear BA, but it isn't very practical. For Single Linear BA on floor at front wall not only the back, but also the top surface (the latter is usually called the ceiling)) in the room must be LF absorber. DLBA is not realistic at all, except that the room has such a shape:

#### Flaesh

##### Senior Member
So for a constant acoustic pressure vs. frequency, the acceleration amplitude of the piston must be constant with frequency as well.
For plane wave the velocity amplitude of the piston must be constant with frequency, I think so.

p. s.:

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#### andyc56

##### Active Member
I am in the process of moving so I will get back to this later. The sound field to look up is the that of a tube, not an infinite baffle.

I am not trying to argue that this response shape can be predicted from the radiation of a piston in an infinite baffle into half-space. My question was about the nature of the stimulus used in the simulation itself.

So why should I care about "radiation of a piston in an infinite baffle into half-space" then? Because that's how the on-axis pressure at a point at distance d from the piston is calculated using the Thiele/Small theory. For an ideal sealed or infinite-baffle subwoofer with zero voice-coil inductance, in the T/S theory the passband is the frequency region for which the acceleration amplitude is constant with frequency.

For such a sub, with an applied voltage having a constant amplitude vs. frequency:
• The displacement amplitude vs. frequency has a low-pass characteristic
• The velocity amplitude vs. frequency has a bandpass characteristic
• The acceleration amplitude vs. frequency has a high-pass characteristic (same as the pressure response of the sub itself)
This nature then becomes relevant when such a sub is placed in multiples in a DBA. One might rightly wonder how the subs' response according to the T/S theory is modified by the DBA. I would argue that, to determine such an effect, such a simulation would best be done with a stimulus having a constant acceleration amplitude with frequency.

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