Multiple Small Subs - Geddes Approach - Page 52 - diyAudio
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diyAudio Member

Join Date: Aug 2004
Location: US
Quote:
 Originally posted by gedlee John we've had this agrument before and I still don't agree. Yes you can seperate off the singularity part, which ends up being the free space Green's function, but what is left, the x(r) is not the same modal solution as the homogeneous solution to the wave equation. It will meet the boundary conditions, however it has a different set of coefficients in the series. I directed you to Morse the last time that you said this. I guess you didn't read it.
This is semantics Earl. I never said anything about the form of X(r). But it's a smiple matter that if A = B + C and B is the direct sound from a point source and A is the total response including the reverberation, then subtracting of the direct field can only leave that fraction of the solution which represented the boundary conditions which give rise to the reflections. That is also right out of Morse, (in my own words).

Quote:
 Originally posted by gedlee Clearly the code has some problems since it is fundamental that this cannot occur. I've mentioned before that we don't get the same results doing the same problem.
No there is not a problem. I've verified my code against FEM where possible. As you said in an earlier post, to paraphrase, the higher order modes don't contribute much to the low frequency response therefore only a few modes need be considered for low frequency. I find that to be true. If I run the modal index form 0 to 5 I see very little difference below 100 Hz compared to running the indexes for 0 to 10. So it seems quite reasonable that if I run the indexes from 5 to 10 the low frequency should drop off in general.
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John k.... Music and Design NaO dsp Dipole Loudspeakers.

diyAudio Member

Join Date: Jan 2009
Quote:
 Originally posted by gedlee So the number of modes would be 35 x 35 x 35? Or did you just do 2-D? 35 x 35. At any rate, I think that you and I agree that the direct field does not influence the results and that getting a spatially smooth response allows for global EQ correction, if EQ is used at all. This, to me, is the crux of the situation and I think that we are in complete agreement. Correct? How one achieves this may be different and I am sure that there are a myriad different algorithms, etc. that one can use, but in the end the goal is the same. To me, personally, once the bass response is smooth, you are 90% of the way there. This spatial bass stuff may well be valid, I think that the jury is still out, but one has to have a smooth bass response first and formost before anything further can be considered.
3-D

Yes, I agree wholeheartedly with these points.

diyAudio Member

Join Date: Dec 2004
Location: Novi, Michigan
Quote:
 Originally posted by john k... but changing the position of the source or listener greatly effects the low frequency level. No there is not a problem.
If you switch the source and the receiver the response has to remain the same. I thought you said it changed (which is wrong), but I think I misinterpreted your statement. Do you mean moving the source OR moving the receiver changes the LF level? (Now that I reread it I can see that's what you meant). In a normal room of course this would happen. Or do you mean even when there are no modes? In that case it does seem odd.

I'm still at a loss to understand what you are getting at.

Todd and I have studied this problem as much, if not more, than anyone else on the planet. We see things exactly the same. But you seem to disagree and I'm having trouble understanding why.

diyAudio Member

Join Date: Dec 2004
Location: Novi, Michigan
Quote:
 Originally posted by john k... I never said anything about the form of X(r).

You did say that it was a solution to the homogeneous wave equation in a rectangular room. That's not correct. The solution of the homogeneous wave equation is an infinite set, of eigenfrequencies and eigenmodes, it IS NOT a series with set coefficients. The series only comes about when there is a source - the inhomogeneous solution. The set of coefficients for this series is well known, you show it yourself. When the free space Greens function singularity is subtracted off, a new series remains, but with a different set of coefficients. However, this new series IS NOT a solution of the homogeneous wave equation - its a series, not a set - and so it cannot be X(r) as you have defined it.

Maybe it is semantics, but then why not just say it correctly.

diyAudio Member

Join Date: Aug 2004
Location: US
Quote:
 Originally posted by gedlee You did say that it was a solution to the homogeneous wave equation in a rectangular room. That's not correct. The solution of the homogeneous wave equation is an infinite set, of eigenfrequencies and eigenmodes, it IS NOT a series with set coefficients. The series only comes about when there is a source - the inhomogeneous solution. The set of coefficients for this series is well known, you show it yourself. When the free space Greens function singularity is subtracted off, a new series remains, but with a different set of coefficients. However, this new series IS NOT a solution of the homogeneous wave equation - its a series, not a set - and so it cannot be X(r) as you have defined it. Maybe it is semantics, but then why not just say it correctly.
From Morse

Quicky derivation of the wave equation for sinusoidal pressure.

Sure looks like the eqaution for X(r) to me. I'll stick by what I said, X(r) is a solution to the homogeneous wave equation with approppriate boundary conditions. Do I need to add the subsctipt, omega, to X(r)? Do I need to say a eignvalue problem requires an eigensolution? Are youy really telling me that since I know gw(r|ro) and I have a modal expansion for Gw(R|ro) I can't directly compute Xw(r) by subtraction for what ever frequency I desire? Do I need to write it down and post a picture?
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John k.... Music and Design NaO dsp Dipole Loudspeakers.

diyAudio Member

Join Date: Aug 2004
Location: US
Quote:
 Originally posted by gedlee I'm still at a loss to understand what you are getting at. Todd and I have studied this problem as much, if not more, than anyone else on the planet. We see things exactly the same. But you seem to disagree and I'm having trouble understanding why.
I think we all have the same goal, smooth bass response. But I don't think you and Todd are on the same page as to how to achieve it. It is clear from Todd's paper that his 4 woofer array is positioning to remove low frequency modal effects from the response.

Quote:
 This configuration should result in cancellation of all odd order axial modes and cancellation of the first even order axial mode.
This is in the plane of the floor. In reality a lot more modes are canceled, for example even order axial modes of order 6, 10, 14.... since these axial modes have nulls at the same location as the 2nd order axial mode. And there are a number of tangential and oblique modes that drop out as well. So I see Todd as looking to limit modal influence where as your approach is ad hoc push the woofers around to yield the smoothest response. You have said a number of time that elimination of modal contributions will not result in good sounding bass. That you want "big room bass". I don't see that as the same. If it is, Todd please correct me. If I look at it differently it is because I have no bias or preconceived notions. I'll look at the physics and come to my own conclusions.
__________________
John k.... Music and Design NaO dsp Dipole Loudspeakers.

diyAudio Member

Join Date: Jan 2009
Quote:
 Originally posted by john k... I think we all have the same goal, smooth bass response. But I don't think you and Todd are on the same page as to how to achieve it. It is clear from Todd's paper that his 4 woofer array is positioning to remove low frequency modal effects from the response.
I'll let you guys argue the maths, I probably am leaning more towards an engineering approach to things. I'm defining a goal (consistent bass response in the seats) and looking for the best solution.

The first paper (placement only) I would say that it does reduce modal excitation, however in SFM it makes more sense to say that the optimization simply tweaks the modal excitation to optimize the result at a few particular locations. I have found that the low frequency response in a room is much more complicated than one might think from the simple mode diagrams on a napkin that we all know and love (for their simplicity). For example, I have observed that the largest cancellations in the frequency response often occur between eigenfrequencies. Also the dips in the spatial response in the room exist and move around not just at the eigenfrequencies, but at frequencies near them. So, in general the response is more complicated than many realize. That's why I say that at least for SFM, saying it just reduces modal excitation might be an oversimplification.

 31st January 2009, 11:29 PM #518 diyAudio Member     Join Date: Aug 2004 Location: US Hi Todd, I would call it arguing. It' just healthy discussion. From my seat it all very clear. If G is the green's function for the in room response, which includes all the boundary effects, and g is the free space (or unbounded) Green's function, and X the correction to the free space Green's function which brings in the boundary conditions then once I have an expression for G, and knowing g, I don't have to solve the wave equation to find out what X is. It's a simple matter of subtraction. It's like if I know between you and I we have \$10 and I know I have \$4 I don't need to ask you how much you have. Obviously some mathematician went through the trouble solving the wave equation for X in the process of coming up with the modal expansion for G. I don't see the need to repeat it. But I do know that as a result, X = G - g allows be to find the value of X(r) for andyvalue of r in the bounded region. Also, remember that g is a smooth exponential g = 1/(4 Pi R) exp(ikR) So all those modes in the summation form of G ultimately arise from X. And there in lies another observation. Note that my quote from Morse says that if there are no boundaries X = 0. That is we have G = g = free space response = spatially smooth bass with only level dependent on listening distance. So in my mind the objective should be how to we make the room look like X = 0, at least from the point of low frequency reproduction. If that produces bass that is subjectively unsatisfactory, well that is a separate issue. But if you approach the problem form the other direction while you might get acceptable smooth low frequency amplitude response the time response will still be a mess. I've shown that by looking at the amplitude response at a given point in a room, equalizing to to match some woofer target response, then computing the impulse response and comparing it to the impulse of the target. The result is that even though the amplitude is good, the impulse is highly distorted, and generally rings well past the decay time for the target. Here is a sample result. The woofer is equalized to a 20 Hz Q= 0.5 HP and 120 Hz B4 LP. Green is what the impulse of such a response would look like in free space. Blue, in a room. I guess I just don't believe that booOOooooooom is going to sound better than Boom. __________________ John k.... Music and Design NaO dsp Dipole Loudspeakers.
 1st February 2009, 06:12 AM #519 diyAudio Member     Join Date: Mar 2005 Location: Taiwan booOOooooooom is going to give an impresson of more boom than Boom. Some people think it's better. It creates a more sensational experience even though it may not be real. Additionally, when at frequencies below the room modes, it becomes difficult to get the Boom effect so there needs to be a way of creating it. __________________ Hear the real thing!
 1st February 2009, 03:14 PM #520 diyAudio Member     Join Date: Aug 2004 Location: US Hi George, My response would be that once you achieve Boom you can manipulate it to boOOooom or what ever you like (BOooOOooom) fairly easily. But going the other way is very difficult. That, I believe, is exactly why we see these different attempts at low frequency response in small rooms with different people claiming theirs is the best approach. Even the approach I have recently experimented with, while moving is the direction I think is correct, has significant limitations and flaws. The only approach I have seen that moves unilaterally in the correct direction (IMO, according to my simulations) in terms of both amplitude and time response is the DBA. The argument that it is impractical, or inefficient are implementation issues and not something that concerns me. I can tell you right now that I will at some point set up a DBA 4x4 system and listen to it before I pass any judgment on it. __________________ John k.... Music and Design NaO dsp Dipole Loudspeakers.

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