Multiple Small Subs - Geddes Approach

[markus76]

Originally posted by gedlee
I would not assume that DBA is the defacto standard that one wants to achieve. That would have to be shown. As I have said, I think that the premise of creating a plane wave in a free field is flawed.

I never said that DBA is the defacto standard but a DBA flattens the frequency response AND eliminates modal ringing at the same time. That is an exessively elaborate thing to do with conventional LF absorption. But by the way, this is exactly what you recommend: high amount of LF absorption (to reduce modal ringing) and multiple subs (to smooth frequency response).

If I understood you right, then your newer idea is to make an acoustically small room behave like a much larger space. But how large? Free space? Then we're talking about a DBA again.

Best, Markus

[john k...]

If I take the meaning of acoustically large in the usually sense it would mean that the low frequency cut off was above the Schroeder frequency. Thus we would hear the direct sound plus a relatively smooth reverberant field.

[markus76]

Originally posted by cap'n todd
Once you get the response at different seats similar, you can successfully equalize.

So that's what SFM is all about? Get the frequency response at different seats similar (how similar and by changing what parameters?) and then equalize one so all of them get equalized accordingly? I don't have the feeling that this really works because even if you just want to equalize one single location the equalization has to be very precise to show substantial improvement.

Best, Markus

[gedlee]

Originally posted by john k...
If I take the meaning of acoustically large in the usually sense it would mean that the low frequency cut off was above the Schroeder frequency. Thus we would hear the direct sound plus a relatively smooth reverberant field.

John

I still don't follow.

Your equation for the modal room solution is incorrect in that the direct field is contained in the summation. Adding it on seperately is incorrect. I have written about this many times (ASA, AES) and even sent this in to the AES as Todd Welti got this wrong in his paper too. Its clearly spelled out in Morse that the direct field appears in the summation, but only after a very large number of modes have been summed. High mode numbers for LF signal don't add anything in the reverberant field, but because they are all in phase at the source they do add up to yield the proper near field solution.

[john k...]

Originally posted by gedlee


John

I still don't follow.

Your equation for the modal room solution is incorrect in that the direct field is contained in the summation. Adding it on separately is incorrect. I have written about this many times (ASA, AES) and even sent this in to the AES as Todd Welti got this wrong in his paper too. Its clearly spelled out in Morse that the direct field appears in the summation, but only after a very large number of modes have been summed. High mode numbers for LF signal don't add anything in the reverberant field, but because they are all in phase at the source they do add up to yield the proper near field solution.

Earl,

Yes, I know. I was counting on you to bring that up. I wrote it that way for Todd because that is what he used in his paper and it is also what Walker did in his (1992) BBC report. Both are technically incorrect. I was actually quite surprised to see such an error. As you note the modal expansion is the complete solution to the wave equation for a point source in a room with rigid walls or, at least wall with finite, but small admittance. Morse also point out the the transient response at the listening position can be obtained by taking the IFFt of the frequency response. It follows that the reflection free part of the response is contained in the early time part of that transient.

The problem is that the modal expansion(well at least this expansion) to Green's function for the room does not apply for the case where wall conductance or damping is large (high damping), such as an anechoic chamber (as you have also pointed out in the past). The correct solution for Green's function in an anechoic room would be one that considers boundary conditions which provide for no reflection at the walls; complete dissipation of the incident energy as heat. That solution, at interior points of the room, is identical to the free field Green's function. Thus, I believe that this direct contribution was added by Walker as sort of a fudge. In a highly reverberant room the modal expansion is valid and dominates the solution. If the damping is very high the modal expansion indicates that there is no sound in the room at all, except from the DC(?) mode, which is obviously in error since we know in such an environment we would still hear the direct sound. So the modal contribution dominates at low damping and the free filed solution dominates at high damping and in between the argument is that the solution should be between the extremes. I'm not at all comfortable with that.

But I still stand by the post. If you drop the direct contribution you are still faced with the fact that the inner summation is fixed once the source positions, amplitude and phase are specified and the spatial variation in the sound is a function of the values of the eigenfunctions at the listening position. If you start by placing a woofer in a corner then all modes are excited equally (assuming a rigid room) since they all have a magnitude of 1.0 with phase either 0 or 180. Adding additional woofer can not excite more modes. It can only change the amplitude of the modes. Adding more woofer can only change the inner summation over the sources. But no matter what is done, we are sill subject to the variation of Phi(n,ro) as the listening position, ro, changes.

[gedlee]

John

I follow your math discussion of course, thats not an issue, but I don't follow the significance of what your saying. As you say, with a sub in the corner all modes are excited and that adding more sources can only change the amplitude of those modes. But this is exactly what we want to do right? - change the amplitude of the modes such that they are uniform - smooth - in both space and spectrum. Thats what correctly setup multiple subs does.

[cap'n todd]

Originally posted by markus76


So that's what SFM is all about? Get the frequency response at different seats similar (how similar and by changing what parameters?) and then equalize one so all of them get equalized accordingly? I don't have the feeling that this really works because even if you just want to equalize one single location the equalization has to be very precise to show substantial improvement.

Best, Markus

It may not work perfectly, but do you not accept that it's an easier job if the resposnes a the seats are more similar (and look back at the plots in the paper to see how similar I mean)? As to your second statement, I agree in one sense. If you are using a parametic filter on a high Q peak, the frequency setting should be very precise indeed. As for the Q, less precision is required, and for the cut, you just need to bring the peak in question down to approximately the same level as other peaks (IMHO of course, but I have done some investigations).

[cap'n todd]

Originally posted by john k...



Earl,

Yes, I know. I was counting on you to bring that up. I wrote it that way for Todd because that is what he used in his paper and it is also what Walker did in his (1992) BBC report. Both are technically incorrect.

Yes, after Earl pointed that out to me I did some further investigations and found that I couldn't even calculate a high enough mode order to see any evidence of the direct field show up. So, given the need to use a reasonable order calculation, the "fudge" seems reasonable. Also, though I have not tried to wade through Morse, as I understand it there are a number of simplifications and assumptions inherent in even that mathematical treatment.

[MartinQ]

I did a quick scan of the previous pages but could not find what SFM stands for.

???

[john k...]

Originally posted by gedlee
John

I follow your math discussion of course, thats not an issue, but I don't follow the significance of what your saying. As you say, with a sub in the corner all modes are excited and that adding more sources can only change the amplitude of those modes. But this is exactly what we want to do right? - change the amplitude of the modes such that they are uniform - smooth - in both space and spectrum. Thats what correctly setup multiple subs does.

Earl,

The inner sum is the contribution of the room-listener transfer function from the eigenfunctions at the source positions. You can manipulate that as you like. But the other factor is the eigenfunction at the listening position. You have no control over that. So what is smooth at one point can not be at another.

Originally posted by cap'n todd


Yes, after Earl pointed that out to me I did some further investigations and found that I couldn't even calculate a high enough mode order to see any evidence of the direct field show up. So, given the need to use a reasonable order calculation, the "fudge" seems reasonable. Also, though I have not tried to wade through Morse, as I understand it there are a number of simplifications and assumptions inherent in even that mathematical treatment.

I think Earl misspoke a little. You can not recover the direct sound just by increasing the number of modes. What you recover is wider frequency response. The direct sound is only recovered when the listening position is very close to the source position just as you would recover the direct sound with a near field measurement. Then given that wide range frequency response you can IFFt it to obtain the room impulse. From that the reflection free response can be obtained, but only if the impulse is windowed to a time less that that of the first reflection, as if you are doing a windowed MLS measurement. You can recover the direct sound at low frequency any more than you can measure it in a reverberant room. For example, the impulse response the a Q = 0.707 25 Hz HP response extends well past 50 msec. That's a propagation distance of 56 feet.

The only way you will see the direct sound at low frequency show up is to eliminate the low frequency modes.

Here is a figure. But the caption should read 0.01M from source for the flat response.





Here is another simulation. The listening position has changed a little (I didn't remember the exact location of the original location) but is still about 3 M form the source. The orange curve is the same setup as the pink one but, through the magic of simulation, the DC and first 3 modes in each direction are omitted (and tangential and orthoganol modes dependent upon them). The upper limit of for the modes for the ornage trace was higher than for the blue trace, hence more high frequency response. But you can see that when the low frequency modes are not present the low frequency response is flat. I.E. don't excite the lo frequency modes if possible.