Multiple Small Subs - Geddes Approach

[john k...]

Hi Todd,

I include a high pass response in the sims to represent the woofer TF.


In the paper the 1/4 spacing 4 woofer array result does not show separate direct and total responses.

All modes roll off 12dB/oct. But it is necessary to consider from what amplitude. The form is 1/(Kn^2 - k^2). For DC mode Kn = 0 and the roll off is from an amplitude of infinity. For all other modes, below Kn the level is proportional to 1/Kn^2. Here Kn = eta - i x (damping function). Thus at low frequency the DC mode can contribute more to the response than a higher order mode does.

Anyway, I have looked again at the results and I find that while my sims are not exactly comparable to your, probably due to differences in how we treat the damping, the variation with position is similar to your result. Apparently I am impaired with regard to typing input, or at least getting it in the correct order. Fixed that and things look much better.

I don't need you code but could you provide me with your damping formulation?

By the way, my results show very little difference if I include or exclude the direct term.

[cap'n todd]

Originally posted by john k...


Thus at low frequency the DC mode can contribute more to the response than a higher order mode does.

Right, but it sounded ike you were saying the opposite in your last post.

Originally posted by john k...

Anyway, I have looked again at the results and I find that while my sims are not exactly comparable to your, probably due to differences in how we treat the damping, the variation with position is similar to your result. Apparently I am impaired with regard to typing input, or at least getting it in the correct order. Fixed that and things look much better.

I don't need you code but could you provide me with your damping formulation?

Thats good, at least not too different. I'm not sure what you mean by damping formulation. As I said it's just the equations from Walker. I implemented a series of nested loops. Perhaps this is part you refer to:
if nx == 0;ex = 1;else ex = 2;end
if ny == 0;ey = 1;else ey = 2;end
if nz == 0;ez = 1;else ez = 2;end
damping = c*((ex*ax+ ey*ay + ez*az))/(16*Vm);

Originally posted by john k...

By the way, my results show very little difference if I include or exclude the direct term.

I get the same. I cant remember if any of my published plots show the direc and modal, but it seems that usually the direct only affects the dips of the modal response (either adding or cancelling, but usually adding).

[john k...]

Right, but it sounded ike you were saying the opposite in your last post.

When I say low frequency I did not mean to limit that below the first finite mode. For example, the (0,0,0) mode can contribute more to the response than the (4,0,0) mode at frequencies just below the that of the (4,0,0) mode. If you plot out the contribution form each mode this is pretty obvious.

if nx == 0;ex = 1;else ex = 2;end
if ny == 0;ey = 1;else ey = 2;end
if nz == 0;ez = 1;else ez = 2;end
damping = c*((ex*ax+ ey*ay + ez*az))/(16*Vm);

What I was referring to is the a's. These are related to the absorption coefficient, alpha:

ax = 2 x Ly x Lz X alpha, etc.

So I was wondering about how you arrived at the alpha, which is frequency dependent. Earlier you said something about sheet rock.

I also look at an order of magnitude analysis of the damping which indicated that the requirement for alpha is that

alpha << n x Pi.

[cap'n todd]

Hi John, about the contribution of modes, I have plotted modal versus 0,0,0 only and based on observation concluded that the 0,0,0 had a 12 dB/oct rolloff and everything else was riding on that. You say that all modes have the rolloff. I'll have to scrutinize the equation a bit more, but my plots don't seem to show that. Here's on where i added the 0,0,0 (blue). If the modal resposne for > 0,0,0 modes was also rolling of at 12 dB/oct, the entire resposne would be. I must be missing something (wouldn't be the first time!)

As for alpha, yes I'm using fixed per frequency (but I'm only looking below 100 Hz or so anyway):

ax = (2*Ym*Zm)*alphax;
ay = (2*Xm*Zm)*alphay;
az = (2*Xm*Ym)*alphaz;

I used 0.05 for all alphas

[auplater]

Originally posted by cap'n todd
Hi John, about the contribution of modes, I have plotted modal versus 0,0,0 only and based on observation concluded that the 0,0,0 had a 12 dB/oct rolloff and everything else was riding on that. You say that all modes have the rolloff. I'll have to scrutinize the equation a bit more, but my plots don't seem to show that. Here's on where i added the 0,0,0 (blue). If the modal resposne for > 0,0,0 modes was also rolling of at 12 dB/oct, the entire resposne would be. I must be missing something (wouldn't be the first time!)

As for alpha, yes I'm using fixed per frequency (but I'm only looking below 100 Hz or so anyway):

ax = (2*Ym*Zm)*alphax;
ay = (2*Xm*Zm)*alphay;
az = (2*Xm*Ym)*alphaz;

I used 0.05 for all alphas

[auplater]

Wondering what the practical goals of all these simulated responses are? What with the assumptions about, for instance, eigenmode amplitude approximations (seeing as the theory implies infinite impulse and zero width), room boundary condition compromises, room dimensional constraints, all conditioned by the model, what are the real world applications, or is this just an academic exercise.

Seems Dr. Geddes has been doing the math, as well as empirical work for over 2 decades, developed award winning speakers as well as an eminently usable semi-empirical method for subwoofer placement, and tirelessly worked to explain to others his rational based on theory.

So I'm not sure what the use of these sims in real home listening environments is, seeing that this is Geddes subwoofer approach thread.

John L.

[cap'n todd]

Originally posted by auplater
Wondering what the practical goals of all these simulated responses are? What with the assumptions about, for instance, eigenmode amplitude approximations (seeing as the theory implies infinite impulse and zero width), room boundary condition compromises, room dimensional constraints, all conditioned by the model, what are the real world applications, or is this just an academic exercise.

Seems Dr. Geddes has been doing the math, as well as empirical work for over 2 decades, developed award winning speakers as well as an eminently usable semi-empirical method for subwoofer placement, and tirelessly worked to explain to others his rational based on theory.

So I'm not sure what the use of these sims in real home listening environments is, seeing that this is Geddes subwoofer approach thread.

John L.

If you read the thread, you'll see that in my case, the abosrption is is not zero, but approximatley equal to the absorption of sheetrock at low frequencies. Earl has also done simulations, and John and I have also done real world measurements. They are both are useful if you know what the limitations are. That's what much of these discussions is about.

[john k...]

Originally posted by cap'n todd
If the modal resposne for > 0,0,0 modes was also rolling of at 12 dB/oct, the entire resposne would be. I must be missing something (wouldn't be the first time!)

Neglecting damping the form of any mode is 1/(Wn^2 -W^2) which is a 2nd order lowpass response with corner frequency Wn and pass band amplitude proportional to 1/Wn^2.



below 55 Hz or so the (0,0,0) mode contributed more to the response that the (0,4,0) mode. Both ultimately roll off 2nd order.

[auplater]

Originally posted by cap'n todd


If you read the thread, you'll see that in my case, the abosrption is is not zero, but approximatley equal to the absorption of sheetrock at low frequencies. Earl has also done simulations, and John and I have also done real world measurements. They are both are useful if you know what the limitations are. That's what much of these discussions is about.

Hi Todd..

Not trying to be difficult or contrary (and I've been trying to follow the thread)... just trying to figure if the math can be manipulated and or massaged to help with improved music quality in my setup.

I currently have 3 12" sonosubs in various ported configurations, a dual 10" isobaric BR, plus dual 6" mid subs in main 6' dipoles, plus 10" woofers in old Advent 6002's for sides in 7.1 configuration.

After moving subs around per (more or less) Gedde's type arrangement methodology, I've achieved reasonably smooth (by ear and rudimentary measurement in ARTA) bass response at SOME locations in the room, but the primary listening (for both music and HT) doesn't have the same quality of DEEP bass as the perimeter areas (roughly a horseshoe shaped region 16' back and maybe 20' wide of high modal intensity below maybe 40 Hz or so) with an additional punch and/or palpable attack that's kinda hard to describe except that it sounds like what deep bass sounds like in a large rock concert arena (maybe the 0'th mode room pressurization?).

So I'm trying to perhaps de-cypher the math well enough to see if modifications of the transfer function for the room would translate to physical location and/or subwoofer/room parameter changes to somehow move the modal behavior I like to the area where I want it. I really don't want to watch movies or listen to music from the sides where the bass is best, but outside of the "sweet spot" for imaging/directivity, etc.

hence the questions as to how to apply the series reduction of Green's function to the real world situation. Unfortunately, of all my present and former professional affiliations, AES isn't one of them, so I don't have access to peer reviewed articles on the subject.

maybe mathematical modal behavior



Not to mention my calculus is 30 years rusty... D

John L.:

[cap'n todd]

Originally posted by john k...



Neglecting damping the form of any mode is 1/(Wn^2 -W^2) which is a 2nd order lowpass response with corner frequency Wn and pass band amplitude proportional to 1/Wn^2.



below 55 Hz or so the (0,0,0) mode contributed more to the response that the (0,4,0) mode. Both ultimately roll off 2nd order.

Oh, I was thinking the entire modal repsonse, not a single mode. Separating out one mode like that is even more theoretical than some of the other stuff we have been discussing. No physical standing (even just two walls) wave would ever have that response, since there would always be standing waves at harmonics of the first on (95 hz in your plot). but anyway I see what you are saying.

I think there is some confusion between a mode and a resonance (even to me). I hold that a mode refers to the spatial standing wave, which will never look like the plot you showed. That would more properly be called a resonance.