I said I would post this a few days ago. These are simulation of, top, a DBA, remaining, 4 woofer array with 1/4 spacing on the floor. All cases are for a room 20'W x 26'L x 9'H. This is the room size used in the Harman paper. All rooms are assumed perfectly rigid and sealed with no damping. The pink trace is the result for a single woofer located in a corner with the listener at some arbitrary position which, unfortunately, I forgot to make note of. However, it is just for a reference so it really doesn't matter too much.
The DBA shows that regardless of where the listener is, unless very close to one of the sources, the behavior is the same everywhere. There are no modes below 100 Hz excited other than the DC mode. There are some higher order modes above 100 Hz excited which have a slight effect on the response just below 100 Hz but this is fairly minor. Note that the effect of the DC mode is a rising response at 6dB/octave. This is correct and a result of the delay applied to the rear woofers. It is the same effect as seen with an unequalized cardioid woofer.
The lower 4 figures are for the 4 woofer, 1/4 spacing array. Here we see that as indicated on the Harman paper, the low frequency modes are not excited. The first excited mode is at 63 Hz which is the axial mode in the vertical direction and consist en with the Harman paper. The next excited mode is at about 85 Hz which does not agree with the Harman paper. This mode is the 4th axial mode in the lengthwise direction and should be expected to be excited by such an array. The Harman paper shows an excited mode at 95 Hz, so perhaps this was a plotting error. We also see cancellations due to the interaction of room modes. The frequency of these cancellations is dependent on listener location. Adding damping to the results would reduce the level of the excited modes and "fill in" the nulls to some extent, but position dependents would still be present.
Failure to excite low frequency modes will means that the response would be void of room effect over the low frequency range. If these rooms leaked and failed to excite the DC mode we would also expect to see the contribution form the DC mode reduced at low frequency. Whether the reduction in modal excitation leads to more or less accurate/satisfying bass response is another issue, likely depending on the intended application of the woofer system (HT or music) and personal preferences.
The DBA shows that regardless of where the listener is, unless very close to one of the sources, the behavior is the same everywhere. There are no modes below 100 Hz excited other than the DC mode. There are some higher order modes above 100 Hz excited which have a slight effect on the response just below 100 Hz but this is fairly minor. Note that the effect of the DC mode is a rising response at 6dB/octave. This is correct and a result of the delay applied to the rear woofers. It is the same effect as seen with an unequalized cardioid woofer.
The lower 4 figures are for the 4 woofer, 1/4 spacing array. Here we see that as indicated on the Harman paper, the low frequency modes are not excited. The first excited mode is at 63 Hz which is the axial mode in the vertical direction and consist en with the Harman paper. The next excited mode is at about 85 Hz which does not agree with the Harman paper. This mode is the 4th axial mode in the lengthwise direction and should be expected to be excited by such an array. The Harman paper shows an excited mode at 95 Hz, so perhaps this was a plotting error. We also see cancellations due to the interaction of room modes. The frequency of these cancellations is dependent on listener location. Adding damping to the results would reduce the level of the excited modes and "fill in" the nulls to some extent, but position dependents would still be present.
Failure to excite low frequency modes will means that the response would be void of room effect over the low frequency range. If these rooms leaked and failed to excite the DC mode we would also expect to see the contribution form the DC mode reduced at low frequency. Whether the reduction in modal excitation leads to more or less accurate/satisfying bass response is another issue, likely depending on the intended application of the woofer system (HT or music) and personal preferences.
An externally hosted image should be here but it was not working when we last tested it.
This basically tells me that using active cancellation speakers can provide pretty good results as well. The way DBAs are located, time alignment between the front woofers and main speakers will have some adverse effect, so the issue would be how to obtain a good balance between music transient performance versus room mode cancellation. The wish for capability for SoundEasy to simulate multiple speaker projects in one room was intended to investigate this trade-off.
soongsc said:
You need to look at the math some more. Once the room boundaries have complex impedances, as they must if they are not rigid and are absorptive, then the modes become complex. Any solution which does not allow for complex modes is therefor incorrect. But there is a further complication. Once the modes are complex then they are no longer necessarily orthogonal. Hence one cannot form the Green's function as a series solution to any room with non-rigid walls. Basically once the walls become "sufficiently non rigid" the entire solution fails. So it IS and issue.
janneman said:
the distance to the floor is part of the tuning. when this distance is "large enough" then its no longer a factor. Measuring the impdance would tell you this, but what you state is a decent rule of thumb.
janneman said:
Hi Jan, that someone was Earl. We discussed this in one of the Nathan threads if I recall it correctly. I built my subs (http://www.mehlau.net/audio/sub_peerless_sls-10/) accordingly with casters underneath. The gap is about 5cm.
Best, Markus
pedroskova said:
Just a reference listening room. I believe at t hat time there was 2 layer of sheetrock on the walls so a bit live at the low end.
soongsc said:
Where's the problem? Use a RTA and you know what the noise floor is and what impact it has on your waterfall diagram. In REW it's just one click – it doesn't get easier than this.
john k... said:
Thanks John, quick question before I scrutinize these more. You say no damping. Is there damping from air absorptin then? Of course, that would be very small, but if there is NO damping does the simultation not explode? Or, is it limited in level due to the finite order calculated? My simuations used absorption approximate to a sheetrock wall at low frequencies.
Hi Todd,
Yes, I mean no damping at all. The simulation doesn't explode because I never calculate exactly at a frequency which is equal to the frequency of a mode. Therefore the denominator of each mode in the summation for pressure does not go to zero. In theory the undamped resonance peaks would go to infinity. However, this would not change the appearance (amplitude) of the modal resonance just to each side of the modal frequency, as shown.
Earl is correct, however. This type of modal analysis is based on the assumption that wall admittance (reactance and conductance) is small. Based on how the modal summation is expressed in your Harman paper this translated to you damping, Kn << 1.
I actually reconfigured my code to have the same summation form as you present so there are no differences that can be attributed to different formulations. I did not, however, include the direct contribution in these calculations. My original code is formulated somewhat differently and allows for admittance which has both reactive and conduction parts (wall flexing and damping) as well as complex eigenfunctions.
I'm a little perplexed at to why you do not show an excited mode at 85 Hz (actually 86.86 Hz) and do show one at 95. When I look at the modes between 90 and 100 Hz for your SET up I see that these are tangential or oblique modes who's contribution from the 4 sources should cancel regardless of listening position.
FYI, here is a sim of the DBA in a room with the DC mode excluded. Sort of an approximation to a "leaky room".
Yes, I mean no damping at all. The simulation doesn't explode because I never calculate exactly at a frequency which is equal to the frequency of a mode. Therefore the denominator of each mode in the summation for pressure does not go to zero. In theory the undamped resonance peaks would go to infinity. However, this would not change the appearance (amplitude) of the modal resonance just to each side of the modal frequency, as shown.
Earl is correct, however. This type of modal analysis is based on the assumption that wall admittance (reactance and conductance) is small. Based on how the modal summation is expressed in your Harman paper this translated to you damping, Kn << 1.
I actually reconfigured my code to have the same summation form as you present so there are no differences that can be attributed to different formulations. I did not, however, include the direct contribution in these calculations. My original code is formulated somewhat differently and allows for admittance which has both reactive and conduction parts (wall flexing and damping) as well as complex eigenfunctions.
I'm a little perplexed at to why you do not show an excited mode at 85 Hz (actually 86.86 Hz) and do show one at 95. When I look at the modes between 90 and 100 Hz for your SET up I see that these are tangential or oblique modes who's contribution from the 4 sources should cancel regardless of listening position.
FYI, here is a sim of the DBA in a room with the DC mode excluded. Sort of an approximation to a "leaky room".
An externally hosted image should be here but it was not working when we last tested it.
john k... said:
The room length should be 24' not 26. That, plus a possible 1 Hz plotting error on my part, might account for the 85 vs 95 Hz thingy. Also, I was using N=5 at the time I did that sim, though using a higher value did not have much effect.
I look forward to your plots using a modest damping factor. My code can also do different absorption on different walls (havent thought about if I could put reactive ipedance in or not) but I have not tried it, since that would be a further departure from the assumptions inherent in the model.
BTW you shoud add y axis units on your plots (for posterity if nothing else!).
My plots showed "modal" and "modal" plus direct.
It may be a stoopid question, I dont understand why, even at a non modal frrequency, if there is no absorption, how can there be a steady state? doesn't the energy just build up? Or, if there is no absorption, isn't the Q of each mode infinite, or no bandwidth?!?!?
markus76 said:
Thanks Earl and Markus, I didn't remember where I found that guidance. I have 4.5cm space at the moment. I'll measure the impedance curve, see what that tells me.
Jan Didden
Yep, I should have used 24. The eyes are getting old. 🙂
The model I use allows for the reactive components. But I don't think it's a big deal. Besides I have no idea what I use for the data.
5 dB/division
Yes I see that in one of the plot. What did you use for the direct sound transfer function? It appears to have a pretty steep roll off.
Good point. I'd have to think about it. Off hand I would say that truncating the series to a finite number of terms might have something to do with it. The contribution to the SPL at a frequency well below the modal frequency goes like 1/(wn^2 - w^2), so while wn keeps increasing the contribution for each mode doesn't go to zero until wn goes to infinity. I'm just thinking out loud here, but what's the integral of 1/(x^2 -c) as x goes zero to infinity?
cap'n todd said:
Wall reactance is actually simpler than resistance because it still results in real modes. It is the absorption that presents the biggest problems, because the modes become complex and this is a lot harder to handle (fully complex code, eigenmodes and eigenvalues). Within the assumption that the modes are orthogonal, any wall impedance is handled basically the same way, but the failure of the orthogonality assumption will come arround and bite you in the a__ before very much impedance change is added to the walls. The orthogonality issue is a real problem. Wall impedance causes the modes to couple and energy leaks from one mode to another. This causes the modes to not be orthogonal (if you think about it this should be apparent). This energy leakage effect DOES occur in real rooms but will not occur in a simple simulation. You will not see energy move from one mode to another in any simulation that uses the standard Green's function series solution (like all of us use). But you will see this in real data. It can be seen in the data that Markus has provided.
Simulations can only tell you so much about real rooms, because rooms can easily violate the assumptions. Rooms like mine will clearly violate the models and its exactly those violations that I would contend offer the greatest gain. Its those things that make a room NOT act like a simple room - a modelable room - that improve it the most. You don't learn this from a model.
Yes, reactive wall impedance data is hard to find!
The direct sound was calculated using the equation from Walker. However, I did convolve with a nearfield measured sub response. Myabe thats what you see.
I guess if/since the response at the modal frequency goes to infinity, the bandwidth is infinitely narrow at that EXACT point. Still, it's discontinuous, so hard to conceptualize. Or, as you say its because the nuber of terms in finite.
I'm not sure it makes any sense t use 0 absorption.
I'm at home so no calculus books here. Looked it up on Wolfram's Integrator.
integral is:
-atanh(x/(c^.5)) / c^.5
I get - i * pi/2/c^.5
for integration from 0 to infinity. I have pretty much no doubt thats wrong. I havent done more than one or two integral since college!
The direct sound was calculated using the equation from Walker. However, I did convolve with a nearfield measured sub response. Myabe thats what you see.
I guess if/since the response at the modal frequency goes to infinity, the bandwidth is infinitely narrow at that EXACT point. Still, it's discontinuous, so hard to conceptualize. Or, as you say its because the nuber of terms in finite.
I'm not sure it makes any sense t use 0 absorption.
I'm at home so no calculus books here. Looked it up on Wolfram's Integrator.
integral is:
-atanh(x/(c^.5)) / c^.5
I get - i * pi/2/c^.5
for integration from 0 to infinity. I have pretty much no doubt thats wrong. I havent done more than one or two integral since college!
gedlee said:
Yes, I have seen this many times. Thats why looking at the fine detail of a waterfall can be bewildering. Earl, would your comments about orthagonality relate to the fact that if you have real damping, you technically no longer have a standing wave? i.e. now there is net energy flow.
FYI-
I ran across this product today. It's not really on topic, but I thought it may be of interest to some of you serious about room treatment and/or constrained layer damping:
Green Glue
I ran across this product today. It's not really on topic, but I thought it may be of interest to some of you serious about room treatment and/or constrained layer damping:
Green Glue
cap'n todd said:
When there is damping there is no pure standing wave there is a standing wave plus a traveling wave, just like in a plane wave tube - Standing Wave Ratio. But the damping in the wall impedance is imaginary not real. I don't see the direct connection to orthogonality though.
As far as the modal Greens function goes, the denominator term is (kn^2 - k^2) which is not discontinous (except when kn = k) although it is singular if kn is real, which it can never really be. So there is always a contribution to the pressure from all kn due to any excitation k. Its never zero. Thus there is never a true null in the response except when the numerator goes to zero, except that never really happens either because the modes are complex too and the numerator is never really zero. Your trying to give a rational explaination to an irrational problem.
The near field term from Walker is wrong, I thought that we had settled that already.
gedlee said:
A million thanks to all for your time & effort in this excellent thread.
Probably ridiculous, but I gotta ask. What about one in each front wall corner, floor-to-ceiling cylindrical concrete former (Sonotube), 16-18" diameter? Stuff the cylinder w/ insulation as tightly as possible & seal one end w/ wood. The other end is covered w/ a screen OR put a 15" passive radiator on it?
How much bass damping might the above cylinders provide vs. the recommended false wall placed over the current sheetrock-over-concrete (front wall)? The cylinders would cost less & be portable.
gedlee said:
ok. I thought we agreed that the "direct" term was a fudge, but acceptably small error. That is, assuming a (relatively low) order modal calc is made, then the direct is not included, therefor a simple additional direct term is ok.
What does this have to do with FEA? If the analysis does not match you measurements, then of course the analysis will not be useful. But we won't know until we actually compare, can't we. I think you are just afraid that the analysis reflects the reality of you recommended setup, and thus providing more credibility to john k's analysis.gedlee said: