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Stereo Bass using subwoofers

Um, sound pressure is proportional to f^2 * volume velocity. There's 2 accelerations involved, cone displacement and microphone displacement, reacting to pressure, so from end to end, it's f^2 * displacement. That's why speakers can be flat, after all, the second-order lowpass above resonance works to provide flat reproduction.
I agree that a speaker indeed follows a f^2 relationship due to mass control but is a mic diaphragm not designed to move with velocity proportional to pressure? Because correct me if I am wrong but otherwise the output would increase by 12 dB per octave (20log10(2^2)=20log10(4)=12 dB)?
 
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I don't understand what you're accusing me of.
I am not accusing you of anything, I am just saying your graph presents a suitably time shifted impulse so as to show a min phase response and there must be something wrong about it.
 
I agree that a speaker indeed follows a f^2 relationship due to mass control but is a mic diaphragm not designed to move with velocity proportional to pressure? Because correct me if I am wrong but otherwise the output would increase by 12 dB per octave (20log10(2^2)=20log10(4)=12 dB)?

I'm not sure you've analyzed a diaphragm mike.
 
I'm not sure you've analyzed a diaphragm mike.
Definitely not but I know they all have a flattish response at least in a certain frequency range and don't exhibit a 12dB increase with every doubling of the frequency - actually Audyssey mic kind of does :) Maybe my math is wrong so I am willing to hear your explanation.
 
There's 2 accelerations involved, cone displacement and microphone displacement, reacting to pressure,
Is a condenser microphone diaphragm not stiffness-controlled below its fundamental resonance (~70kHz for the B&K 4136)? If it isn't, B&K should correct their technical documentation ;).
 
I am just saying your graph presents a suitably time shifted impulse so as to show a min phase response and there must be something wrong about it.
It does not show the measured response as being minimum phase and I'm not sure why you think it does. Here's some data which I hope will clear some things up:

I generated impulse responses of two chains of digital IIR filters. One is minimum phase, while the other one is not. More specifically, one has two 2nd-order IIR allpass filters added which have a center frequency of 20Hz and a Q-factor of 0.8. The minimum phase part of both consists of a 4th-order butterworth highpass at 25Hz and a 6th-order butterworth lowpass at 250Hz. I did not time-shift the results in any way—the input impulse is exactly at t=0 in both cases—nor did I change the polarity of either. Here are the magnitude responses:
minphase_demo_magnitude.png
As expected, they are exactly identical. Now the phase responses:
minphase_demo_phase.png
Compared to the red trace (which is minimum phase), the excess phase in the blue trace is clearly seen. Here's the group delay of both:
minphase_demo_group_delay.png
And finally, the impulse responses:
minphase_demo_impulse.png
Both initially go positive, but then diverge. Indeed, the blue trace (non minimum phase) is broadly similar to the measured impulse of the SB-3000, while the red trace (minimum phase) is broadly similar to the minimum phase version of the SB-3000 impulse I had generated.
 
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It does not show the measured response as being minimum phase and I'm not sure why you think it does. Here's some data which I hope will clear some things up:

I generated impulse responses of two chains of digital IIR filters. One is minimum phase, while the other one is not. More specifically, one has two 2nd-order IIR allpass filters added which have a center frequency of 20Hz and a Q-factor of 0.8. The minimum phase part of both consists of a 4th-order butterworth highpass at 25Hz and a 6th-order butterworth lowpass at 250Hz. I did not time-shift the results in any way—the input impulse is exactly at t=0 in both cases—nor did I change the polarity of either. Here are the magnitude responses:
View attachment 433660
As expected, they are exactly identical. Now the phase responses:
View attachment 433661
Compared to the red trace (which is minimum phase), the excess phase in the blue trace is clearly seen. Here's the group delay of both:
View attachment 433662
And finally, the impulse responses:
View attachment 433663
Both initially go positive, but then diverge. Indeed, the blue trace (non minimum phase) is broadly similar to the measured impulse of the SB-3000, while the red trace (minimum phase) is broadly similar to the minimum phase version of the SB-3000 impulse I had generated.
The min phase version of the sub's response vs what I believe to be the filters at work on that sub (there's probably another lpf higher up the band which I ignored):

1741247497212.png


and the most logical match is non-causal (hence non min phase) and "inverted" measured response.

1741247689406.png
 
and the most logical match is non-causal (hence non min phase) and "inverted" measured response.
I disagree completely with the above statement. Here's a more accurate IIR model of the sub:
iir_sub_model_magnitude.png

iir_sub_model_phase.png

iir_sub_model_group_delay.png

iir_sub_model_impulse.png


As before, the two impulses from the IIR models are not time shifted. All are shown with the original (positive) polarity. Please explain why you think the measured impulse should be inverted.
 
Cross correlation align them and see how it shifts.
It looks virtually identical:
iir_sub_model_impulse_xcorr.png

Not sure what you expected to see. This time I didn't remove the small time delay present in the measured impulse.
 
It looks virtually identical:
View attachment 433695
This time I didn't remove the small time delay present in the measured impulse.
I was talking about CC align over the MP version. My guess is their peaks will align and they will be in opposite directions.
 
You are not aligning them to the MP version when it's measurement #3, move it to the top and re-try.
It makes no difference other than removing a bit of delay in the measured impulse:
iir_sub_model_impulse_xcorr3.png
 
It makes no difference other than removing a bit of delay in the measured impulse:
View attachment 433699
Interesting...Then the sub response is causal like min phase, non-invertable but IIR also isn't, just has extra group delay that makes it non-min phase.
 
causal like min phase [...] just has extra group delay that makes it non-min phase
Yes, that can be seen from the slope of the excess phase in post #644. Otherwise, there would be significant sections where the excess phase rotates the other direction (i.e. goes more positive with increasing frequency, ignoring wraps).

Here are some plots that show what it looks like with the allpass component reversed in time (i.e. made anticausal):
reversed_allpass_phase.png
reversed_allpass_group_delay.png
reversed_allpass_impulse.png

Edit: Another thing which I forgot to point out before is that @levimax stated that the measurement was done with a loopback timing reference, so the time offset accurately represents the total time delay from the electrical input to the measured acoustic output. The amount of negative time shift required to align the peaks in your inverted impulse proposal requires that the measured system be acausal. Not "faux acausal" where delay is added to an acausal system to make it realizable in real time, but actually acausal. It is therefore not a valid solution.
 
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I also think multi-sub deployments are more likely to be less punchy as sub count goes up.
I think rooms mask this phenomenon, especially small ones. Bigger the room, the less the masking.
Tactile feel that is more in the mode of steady vibration, like hair tingling, pants flapping, or chest resonating......multi-works just fine ime.
But punch, the hit in the chest, the bass drop that sends loose beers cans flying, comes from a strong vector...which is usually easiest to obtain from a single sub cluster.

Over the last dozen years I've amassed a near ridiculous amount of subwoofer power. (I wanted to partner with some folks for live sound, but found I don't like the late night hours gigs often require.)
Anyway, I've built a lot of subs...sealed, reflex, front-loaded horns...and bought a few more. I've compared then indoors and out, in single, stereo, and multiple sub fashion.
Subs definitely have a directional punch ime. And with multiples it's a vectored punch.

Heck, even a single reflex sub has a directional punch, depending on where the ports are in relation to the cone.
I've built double 18" subs with the ports surrounding the drivers in the front baffle like typical, with ports firing to to floor, with a slot port facing outward between two opposed drivers facing each other clamshell style, and drivers in a 90 degree frontal angle with a large port below them. They all hit a little different, and it's almost track by track which sub will hit hardest on it. (They are were tuned maximally flat to within a few Hz, using the same 18" BMS drivers.)

Anyway again, I know this thread is really in reference to home audio rooms, but it don't think it takes that big of a room, to feel the hit difference from a single sub (with balls) vs multi-subs (also with balls).

You can have a system that does really well but it's the room that surely brings every bit of complexity to the matter, having in mind what @j_j says about velocity and pressure in recent discussion.

It has been my experience that certain strategies can be beneficial for the overall performance and in some cases you should even be careful what you wish for. The overall shape of the wavefront is what may be worth to look into, also having ports or not in the equation may sound and feel very different.

My setup is stereo bass and I've shared some measurements in other threads, but here I would like to focus on the correlated signals, especially ones that may produce the punch you describe. In room front wall and floor bounce must be considered along with wavelengths, room dimensions, where the system and MLP is positioned, etc. It's about how the energy is distributed along the way. Luckily bass is slow and can be manipulated, room gain as well.

Here are some initial measurements from setup and alignment that to me looked deceiving:


- close field, subwoofer cone level, mains ported (no smoothing):


01.jpg


Some colors of that:

03.jpg


Same setup, ear level, 3,5 meters distance:

02.jpg


Which translated into the room that wants to ring forever:


04.jpg


Comparing step response of this and that:

05.jpg


I thought I can do better with regards to time and phase alignment, group delay and all that, so I did:

Again close field, sub cone level:

06.jpg


This looks a bit better:

07.jpg


Unfortunately, this at MLP this was even worse, at which point I started thinking in terms of what amount of energy and at what time can I put it into the room, without making it collapse. This was not about punch, nor trouser flapping, plenty of that, but the room simply could not handle it. Even though there's not much very low frequencies at ear level, all the sub bass was accumulating underneath my seating position, wanting to bring the house down at higher SPL. I've shown measurements of that elsewhere.

Next thing I've done is try and get rid of the ports and this is how it now looks like, with some EQ:

- Close field, sub cone level:

08.jpg



09.jpg


Now, the MLP, ear level:

10.jpg


And how the room behaves now:

11.jpg


I think this deserves a bit of zoom in:

12.jpg


It's slow and predictable distribution of room gain that reaches 6dB louder at MLP that is pretty much frequency independent, caveat being that it comes about 12 ms later. The energy that bounces around is now more predictable, with moments of almost total silence, and then in bounces again but loses pressure more rapidly and more importantly, in similar fashion within modal frequencies as well. Room no longer does what it wants.

The step response of this and that is complicated, to say the least:

13.jpg


And If I clean this up a bit, this is what it does on average at MLP:

14.jpg


How the room behaves seems to be in correlation of where the peak energy level is, so it corresponds to that room dimension in between the system and listening position. The wavefront shape is such that low frequencies can seemingly fit into the room and bounce rather than stand at similar spacing that again corresponds to that 12 ms sound has to travel.

All I can say about how it sounds (and feels like) is that there's plenty of time for localization and neural stream separation, also for auditory compression mechanism to do it's thing. Sense of spaciousness is never confused or masked by that, all important quick bass drops (punches and kicks) or mono centered signals of longer duration. Perhaps @j_j could comment on how do we perceive order vs disorder in low frequencies and how various mechanoreceptors in the body are involved, that would be interesting.
 
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