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31st January 2009, 12:36 AM  #511  
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John k.... Music and Design NaO Dipole Loudspeakers. 

31st January 2009, 01:00 AM  #512  
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Yes, I agree wholeheartedly with these points. 

31st January 2009, 01:05 AM  #513  
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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. 

31st January 2009, 01:28 AM  #514  
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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. 

31st January 2009, 04:15 AM  #515  
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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(rro) and I have a modal expansion for Gw(Rro) 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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31st January 2009, 04:34 AM  #516  
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31st January 2009, 07:26 PM  #517  
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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. 

1st February 2009, 12:29 AM  #518 
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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.
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1st February 2009, 07:12 AM  #519 
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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.
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1st February 2009, 04:14 PM  #520 
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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.
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