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Speaker enclosure vibrations - a few measurements with accelerometer

This are the important frequencies in the tones that music are made of. This has nothing to do with pink noise or sine sweeps.


If the resonances in the cabinet hits one of this specific tone frequencies, it gonna be delayed and the pitch will be slightly altered/ changed in the total sound from the speaker. The result will be that the perceived pitch tonality that you hear will be slightly compromised, and the distinct pitch of the tone will be slightly blurred. Here we can see that the problems with disturbed pitch because of resonances are potentially worse in the lower frequencies than in higher , because of how the tones work.
Our ears are most sensitive in the 2-5 kHz range. So distortion products appearing in that range should be low. Masking is also important so eg 3-5 order distortion is more audible than second. Thus 3-5 order distortion of 500-1000 Hz fundamentals must be very low.
 
Our ears are most sensitive in the 2-5 kHz range. So distortion products appearing in that range should be low. Masking is also important so eg 3-5 order distortion is more audible than second. Thus 3-5 order distortion of 500-1000 Hz fundamentals must be very low.
:facepalm:
 
This link are the important frequencies in the tones that music are made of. This has nothing to do with pink noise or sine sweeps. The human ear has no problem at all to hear a distinct G3 at 196 Hz.


If the resonances in the cabinet hits one of this specific tone frequencies, it gonna be delayed and the pitch will be slightly altered/ changed in the total sound from the speaker. The result will be that the perceived pitch tonality that you hear will be slightly compromised, and the distinct pitch of the tone will be slightly blurred. Here we can see that the problems with disturbed pitch because of resonances are potentially worse in the lower frequencies than in higher , because of how the tones work.
The human sensitivity to hear pitch is very high at 196 Hz , and also far below that frequency.
 
The human sensitivity to hear pitch is very high at 196 Hz , and also far below that frequency.
But the issue is distortion and not pitch. It is well-known that there are dependence on level, critical bands, masking and frequency. Our sensitivity for distortion at bass frequencies are quite low
 
... John Atkinson just explained to you ... There is much confusion in the audio world about ... " ... often add a "wooden" coloration to a speaker's sound.”
C'mon, this seems to be only to keep the pot boiling. Cabinet resonances, if any, conribute exacly nil to the sound. Yes, no problem. Now people die from boredom, nothing to chit-chat about. Heresy, stone him!

Sorry guys, what about dedicated education, creativity and the ability to derive logical conclusions? Anybody? Atkinson, maybe, a person of dedicated interest. "Human perception" etc pp. C/u.
 
C'mon, this seems to be only to keep the pot boiling. Cabinet resonances, if any, conribute exacly nil to the sound. Yes, no problem. Now people die from boredom, nothing to chit-chat about. Heresy, stone him!

Sorry guys, what about dedicated education, creativity and the ability to derive logical conclusions? Anybody? Atkinson, maybe, a person of dedicated interest. "Human perception" etc pp. C/u.
Did you read post 20?
 
I can add a note regarding distortion measurements using microphone measurements, where I found one of my original threads from 2005 in a Swedish forum (time files... now I know how old my speakers are). I measured fixed tones with a microphone and found the following for an older-built enclosure, second and third distortion component.

120 Hz: -48.6 dB (0.37%); -53.2 dB (0.22%)
160 Hz: -51.8 (0.26%); -52.4 (0.24%)
200 Hz: -55.5 (0.17%); -57.9 (0.13%)
250 Hz: -54.3 (0.19%); -63.0 (0.07%)
315 Hz: -54.1 (0.20%); -56.0 (0.16%)
400 Hz: -51.6 (0.26%); -59.4 (0.11%)
500 Hz: -55.3 (0.17%); -38.6 (1.17%)!!!!
630 Hz: -51.7 (0.26%); -58.5 (0.12%)
800 Hz: -56.6 (0.15%); -47.6 (0.42%)
1000 Hz: -51.6 (0.26%); -53.7 (0.21%)

When I built the new constrained layer cabinet I got this:

100 Hz: 0.33%, 0.15%
125 Hz: 0.26%, 0.26%
160 Hz: 0.18%, 0.04%
200 Hz: 0.39%, 0.32%
250 Hz: 0.57%, 1.04%!!!
315 Hz: 0.28%, 0.07%
400 Hz: 0.27%, 0.14%
500 Hz: 0.21%, 0.09%
630 Hz: 0.03%, 0.47%
800 Hz: 0.13%, 0.14%
1000 Hz: 0.13%, 0.39%


So also the acoustic output from the speaker showed distortion components similar to the vibration of the cabinets shown, and shifted from 500 Hz to 250 Hz in the constrained layer cabinet.

Original thread in Swedish:
If you did not change anything else and the result is not due to chance, it is undeniably interesting.:) I wonder if the result would have been the same if you used completely ordinary wood glue?

Same type of wood? Embedding of the driver in the baffle in the same way? Same assembly? Exactly the same shape of the baffle in both cases? Equally tightly screwed in both cases?.. And so on. I just mean everything to rule out factors other than the glue itself.
 
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I can add a note regarding distortion measurements using microphone measurements, where I found one of my original threads from 2005 in a Swedish forum (time files... now I know how old my speakers are). I measured fixed tones with a microphone and found the following for an older-built enclosure, second and third distortion component.

120 Hz: -48.6 dB (0.37%); -53.2 dB (0.22%)
160 Hz: -51.8 (0.26%); -52.4 (0.24%)
200 Hz: -55.5 (0.17%); -57.9 (0.13%)
250 Hz: -54.3 (0.19%); -63.0 (0.07%)
315 Hz: -54.1 (0.20%); -56.0 (0.16%)
400 Hz: -51.6 (0.26%); -59.4 (0.11%)
500 Hz: -55.3 (0.17%); -38.6 (1.17%)!!!!
630 Hz: -51.7 (0.26%); -58.5 (0.12%)
800 Hz: -56.6 (0.15%); -47.6 (0.42%)
1000 Hz: -51.6 (0.26%); -53.7 (0.21%)

When I built the new constrained layer cabinet I got this:

100 Hz: 0.33%, 0.15%
125 Hz: 0.26%, 0.26%
160 Hz: 0.18%, 0.04%
200 Hz: 0.39%, 0.32%
250 Hz: 0.57%, 1.04%!!!
315 Hz: 0.28%, 0.07%
400 Hz: 0.27%, 0.14%
500 Hz: 0.21%, 0.09%
630 Hz: 0.03%, 0.47%
800 Hz: 0.13%, 0.14%
1000 Hz: 0.13%, 0.39%


So also the acoustic output from the speaker showed distortion components similar to the vibration of the cabinets shown, and shifted from 500 Hz to 250 Hz in the constrained layer cabinet.

Original thread in Swedish:
Ok - lets forget how music tones work and concentrate only on static distortion measurements then :

This measurements is , for me at least , evidence that using constrained layer for a loudspeaker cabinet is no garanty for a better sound .
Also :
In a DIY 3- way speaker , those measurements from Thomas points to using 3 different boxes , all 3 different constructed to avoid distortion in the specific frequency area.

In Thomas measurements - with or without constrained layer cabinet, the distortion is higher than 1 % at certain frequencys which is unnaceptable for hifi .

Thomas measurements :

120 Hz: -48.6 dB (0.37%); -53.2 dB (0.22%)
160 Hz: -51.8 (0.26%); -52.4 (0.24%)
200 Hz: -55.5 (0.17%); -57.9 (0.13%)
250 Hz: -54.3 (0.19%); -63.0 (0.07%)
315 Hz: -54.1 (0.20%); -56.0 (0.16%)
400 Hz: -51.6 (0.26%); -59.4 (0.11%)
500 Hz: -55.3 (0.17%); -38.6 (1.17%)!!!!
630 Hz: -51.7 (0.26%); -58.5 (0.12%)
800 Hz: -56.6 (0.15%); -47.6 (0.42%)
1000 Hz: -51.6 (0.26%); -53.7 (0.21%)

When I built the new constrained layer cabinet I got this:

100 Hz: 0.33%, 0.15%
125 Hz: 0.26%, 0.26%
160 Hz: 0.18%, 0.04%
200 Hz: 0.39%, 0.32%
250 Hz: 0.57%, 1.04%!!!
315 Hz: 0.28%, 0.07%
400 Hz: 0.27%, 0.14%
500 Hz: 0.21%, 0.09%
630 Hz: 0.03%, 0.47%
800 Hz: 0.13%, 0.14%
1000 Hz: 0.13%, 0.39%

————

If we look at stereophiles measurements on the Genelec G3, the aluminium cabinet ( high stiffness ) and perhaps the mounting technique from behind the drivers ( clamping the magnet ) is a very good approach how to get good results.
Wooden screws are best avoided ( as i-or already has showed on faktiskt.ie ).
Maybe gluing the drivers to the cabinet is the best way to avoid distortion ?

A6D741A4-C639-4006-8676-2EBDE22DFDDF.jpeg
 
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When I get time I will add some measurements and files showing what is audible and not.
 
Some constructors ( i.e I.Ö ) says it might be an advantage to use different thickness of MDF in the loudspeaker cabinet. If the baffle are made of 22 mm MDF , then it should be better to make the sides of 16 mm and the back of the speaker 19 mm . This avoids the ”tuning fork effect”.
That is a quite reasonable sort of approach to take. However, keep in mind that the resonance frequencies of the side and rear panels are likely to be different simply as a result of their differing dimensions. Dropping the thickness from 19mm to 16mm will reduce the bending stiffness by about 40%, with a 16% reduction in panel mass. Taken together, we could expect a reduction in resonance frequency of about 16%. However, the lighter panel of the two may end up having greater amplitudes of vibration from excitation by the existing energy sources. It's a bit of a tricky area, and probably requires a full modal analysis to make proper sense of.
I have no practical measurement experience of this, but I have tried 3 mm bitumen in some DIY speakers before, also in the jbl 530 , HYBRID and monitor audio rx6, and the best sound results ( better than without bitumen ) was gained with bitumen glued on about 50 % of the loudspeakers internal wall, placed asymetrical , so that the left wall was damped with bitumen and the opposite wall was undamped with no bitumen.
The extra mass of the damping pads will serve to lower the resonance frequency of the panel to which it is attached, as well as damping the flexural vibrations. There will now be a small separation in resonance frequencies, which may serve to make spread resonances less noticeable than a single resonance.
Putting bitumen on all internal walls made the sound much worse in all three loudspeakers.
I wonder why that might have been the case. Maybe a more damped cabinet allowed other problems to be more audible?
Using constrained layer damping would then only be beneficial If used on some of the walls, not all of them.
I'm not entirely sure that is the best course of action. In any case, what was the constraining layer? It would be interesting to know.

The reduction of cabinet wall vibrations is a big plus with constrained layer damping, but it needs a proper constraining layer to produce the high shear stresses in the damping material in order to get the best results. Carefully choosing the thickness and stiffness of the constraining layer is likely to produce the biggest benefits, rather than just not applying damping treatment to some of the panels.
 
That is a quite reasonable sort of approach to take. However, keep in mind that the resonance frequencies of the side and rear panels are likely to be different simply as a result of their differing dimensions. Dropping the thickness from 19mm to 16mm will reduce the bending stiffness by about 40%, with a 16% reduction in panel mass. Taken together, we could expect a reduction in resonance frequency of about 16%. However, the lighter panel of the two may end up having greater amplitudes of vibration from excitation by the existing energy sources. It's a bit of a tricky area, and probably requires a full modal analysis to make proper sense of.

The extra mass of the damping pads will serve to lower the resonance frequency of the panel to which it is attached, as well as damping the flexural vibrations. There will now be a small separation in resonance frequencies, which may serve to make spread resonances less noticeable than a single resonance.

I wonder why that might have been the case. Maybe a more damped cabinet allowed other problems to be more audible?

I'm not entirely sure that is the best course of action. In any case, what was the constraining layer? It would be interesting to know.

The reduction of cabinet wall vibrations is a big plus with constrained layer damping, but it needs a proper constraining layer to produce the high shear stresses in the damping material in order to get the best results. Carefully choosing the thickness and stiffness of the constraining layer is likely to produce the biggest benefits, rather than just not applying damping treatment to some of the panels.
Interesting :).
What about the mounting of the driver to the cabinet ? Maybe gluing are the best?
We miss measurements when this is done, comparing with wooden screws.
 
Interesting :).
What about the mounting of the driver to the cabinet ? Maybe gluing are the best?
We miss measurements when this is done, comparing with wooden screws.
Glue the driver to the baffle? It unfortunately leads to a small problem but okay if you don't intend to remove the driver any more...so why not.

This should be the home street for engineers, physicists to decide, give tips and advice on. There are trainings that focus on such things. Resonances, vibrations, structural dynamics, density in different materials and so on.

This type of training, in:

Structural dynamics is a type of structural analysis which covers the behavior of a structure subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subjected to dynamic loading. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis.

Structural analysis is mainly concerned with finding out the behavior of a physical structure when subjected to force. This action can be in the form of load due to the weight of things such as people, furniture, wind, snow, etc. or some other kind of excitation such as an earthquake, shaking of the ground due to a blast nearby, etc. In essence all these loads are dynamic, including the self-weight of the structure because at some point in time these loads were not there. The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration in comparison to the structure's natural frequency. If a load is applied sufficiently slowly, the inertia forces (Newton's first law of motion) can be ignored and the analysis can be simplified as static analysis.



And or training in this:

What does a Materials Engineer do?

A materials engineer process, test, and develop materials used to make a large variety of products such as aircraft wings, computer chips, biomedical devices, or even golf clubs. They study and evaluate the structures and properties of metal, composites, ceramics, plastics, and nanomaterials to create new materials that can meet the particular chemical, electrical, and mechanical requirements.


Edit:
It is possible that there are those with such training who have already spoken out in this thread.:)
 
What does a Materials Engineer do?
....
It is possible that there are those with such training who have already spoken out in this thread.:)
I didn't get the training on materials engineering. But isn't it just proposing a complicated, costly if not sophisticated solution before analysing the problem? Is there a problem at all? If so, what is it actually? Might be that one needs an argument to sell an otherwise mediocre design by excellence in carpeting. That can be had cheaper I assume.

When I get time I will add some measurements and files showing what is audible and not.
How could You know what I might recognize as objectionable? One could derive some parameter from measurement and compare to something else. But from experience such simple computation of data regularly doesn't hold true with physiology, let alone with, say 'taste'.

My observations:
  • the resonances seen with knocking are already well damped in conventional designs (MDF etc), concluded from how broad they appear (calc/ 'Q')
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall never correlate with resonances excited by a 'knocking
  • when driven by the speaker, there are never higher modes in that the panel showed phase differences from one measuring position to the other, and the amplitude of acceleration steadily decreases towards the rim
  • when driven by the speaker, the frequency of peaks does not change with stiffening the panel on its own, neither with adding mass to the panel
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall correlate with expectable air column resonances
  • when driven by the speaker, the spectrum of peaks is harmonic ( 1 .. 2 .. 3 .. ) as expected from air column resonances ( while panel resonances would show a quite irregular spectrum e/g 1 ..1,4 ... 2,7 ... )
  • when driven by the speaker, the amplitudes of peaks decrease significantly up to vanishing utterly with dampening the internal air volume by e/g some highly effective Basotect material
You can derive Your own conclusions in the very unlikely case You trust my experiences. I've gone through it, me thinks, using two accelerometers on a twin-head amp and analyser.

My personal conclusion is that most of the panel's acceleration is due to internal air resonance.

Practically the enclosure shall be stiff by internal bracing to begin with. It doesn't suffice to point-connect opposing walls, because the phase of internal air resonance has opposing phase between the panels. Otherwise the panels may be made of 12mm (1/2 inch) MDF to fully comply to needs. Further crucial thing to do is to dampen the air inside strictly, even if a resonance would not show in the membranes output directly. If that eats up bass, just make the enclosure larger.

By the way, somebody measured the panel's contribution already with a deliberately bad design. He used the Green's Function to separate the membrane's and the panels' part at a distance--it was an engineering thesis addressing the mathematics, not the actual speaker. The panels' contribution was found to be tiny tiny at best (or worst, as You may see it).
 
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I didn't get the training on materials engineering. But isn't it just proposing a complicated, costly if not sophisticated solution before analysing the problem? Is there a problem at all? If so, what is it actually? Might be that one needs an argument to sell an otherwise mediocre design by excellence in carpeting. That can be had cheaper I assume.


How could You know what I might recognize as objectionable? One could derive some parameter from measurement and compare to something else. But from experience such simple computation of data regularly doesn't hold true with physiology, let alone with, say 'taste'.

My observations:
  • the resonances seen with knocking are already well damped in conventional designs (MDF etc), concluded from how broad they appear (calc/ 'Q')
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall never correlate with resonances excited by a 'knocking
  • when driven by the speaker, there are never higher modes in that the panel showed phase differences from one measuring position to the other, and the amplitude of acceleration steadily decreases towards the rim
  • when driven by the speaker, the frequency of peaks does not change with stiffening the panel on its own, neither with adding mass to the panel
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall correlate with expectable air column resonances
  • when driven by the speaker, the spectrum of peaks is harmonic ( 1 .. 2 .. 3 .. ) as expected from air column resonances ( while panel resonances would show a quite irregular spectrum e/g 1 ..1,4 ... 2,7 ... )
  • when driven by the speaker, the amplitudes of peaks decrease significantly up to vanishing utterly with dampening the internal air volume by e/g some highly effective Basotect material
You can derive Your own conclusions in the very unlikely case You trust my experiences. I've gone through it, me thinks, using two accelerometers on a twin-head amp and analyser.

My personal conclusion is that most of the panel's acceleration is due to internal air resonance.

Practically the enclosure shall be stiff by internal bracing to begin with. It doesn't suffice to point-connect opposing walls, because the phase of internal air resonance has opposing phase between the panels. Otherwise the panels may be made of 12mm (1/2 inch) MDF to fully comply to needs. Further crucial thing to do is to dampen the air inside strictly, even if a resonance would not show in the membranes output directly. If that eats up bass, just make the enclosure larger.

By the way, somebody measured the panel's contribution already with a deliberately bad design. He used the Green's Function to separate the membrane's and the panels' part at a distance--it was an engineering thesis addressing the mathematics, not the actual speaker. The panels' contribution was found to be tiny tiny at best (or worst, as You may see it).
I was mostly curious, especially about Thomas' results.

Your studies were very interesting I must say!:)

Speaking of resonances when it comes to subwoofers. It seems like a substantial braced box means that the resonance frequencies are pushed up in frequency and if you therefore use a steep LP filter, at least 24dB, at 80-100 Hz, you cut them off, and gets rid of those resonances.
No filling/stuffing is even needed in the subwoofer box. For the subwoofer that is. Full range speakers can definitely need filling/stuffing.

About this good braced::)

Sealed CSS with SPA1000 alternate (2).jpg


 
I think that i-or on faktiskt.se on the ongoing thread there, has a big clue to your question, and its the same one that Linkwitz already has written about, - its about the way the driveunit is clamped to the baffle . The best way seems to clamp the driver from behind at the magnet, this way there is no need for screws directly into the front baffle .

Linkwitz wrote :

A) Drivers with a stamped metal baskets are prone to exhibit a high Q resonance when tightly clamped to the baffle. The magnet moves relative to the voice coil at the resonance frequency. Energy is stored and also readily transmitted from the moving mass of the cone into the cabinet.

B) Soft mounting the driver basket to the baffle using rubber grommets reduces the resonance frequency. A 2nd order lowpass filter is formed that reduces the transmission of vibration energy from the moving cone to the baffle and cabinet. The resonance must occur below the operating range of the driver.

C) If the driver is mounted from the magnet and the basket rim touches the baffle only softly, then the magnet-basket resonance cannot occur and the transmission of vibration energy into the baffle is minimized.

View attachment 223028

My comment: I would continue measuring without any screws on the driver basket , using glue or mounting the driver from behind at the magnet.

View attachment 223040
Now I saw your post. That was interesting. ..touches the baffle only softly..ok but won't it leak then if you don't attach the driver hard to the baffle?

Soft mounting the driver basket to the baffle using rubber grommets reduces the resonance frequency.
That sounds reasonable.:)
 
I didn't get the training on materials engineering. But isn't it just proposing a complicated, costly if not sophisticated solution before analysing the problem? Is there a problem at all? If so, what is it actually? Might be that one needs an argument to sell an otherwise mediocre design by excellence in carpeting. That can be had cheaper I assume.


How could You know what I might recognize as objectionable? One could derive some parameter from measurement and compare to something else. But from experience such simple computation of data regularly doesn't hold true with physiology, let alone with, say 'taste'.

My observations:
  • the resonances seen with knocking are already well damped in conventional designs (MDF etc), concluded from how broad they appear (calc/ 'Q')
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall never correlate with resonances excited by a 'knocking
  • when driven by the speaker, there are never higher modes in that the panel showed phase differences from one measuring position to the other, and the amplitude of acceleration steadily decreases towards the rim
  • when driven by the speaker, the frequency of peaks does not change with stiffening the panel on its own, neither with adding mass to the panel
  • when driven by the speaker, the peaks in the acceleration of a cabinet wall correlate with expectable air column resonances
  • when driven by the speaker, the spectrum of peaks is harmonic ( 1 .. 2 .. 3 .. ) as expected from air column resonances ( while panel resonances would show a quite irregular spectrum e/g 1 ..1,4 ... 2,7 ... )
  • when driven by the speaker, the amplitudes of peaks decrease significantly up to vanishing utterly with dampening the internal air volume by e/g some highly effective Basotect material
You can derive Your own conclusions in the very unlikely case You trust my experiences. I've gone through it, me thinks, using two accelerometers on a twin-head amp and analyser.

My personal conclusion is that most of the panel's acceleration is due to internal air resonance.

Practically the enclosure shall be stiff by internal bracing to begin with. It doesn't suffice to point-connect opposing walls, because the phase of internal air resonance has opposing phase between the panels. Otherwise the panels may be made of 12mm (1/2 inch) MDF to fully comply to needs. Further crucial thing to do is to dampen the air inside strictly, even if a resonance would not show in the membranes output directly. If that eats up bass, just make the enclosure larger.

By the way, somebody measured the panel's contribution already with a deliberately bad design. He used the Green's Function to separate the membrane's and the panels' part at a distance--it was an engineering thesis addressing the mathematics, not the actual speaker. The panels' contribution was found to be tiny tiny at best (or worst, as You may see it).
You can see from the measurements on page 1 that the distortion shows up in several peaks. The fundamental from top side of enclosure:

fundamental.png

And second and third harmonics:
distortion.png


With respect to internal dimensions for calculating standing waves the inner distance between top and bottom is 0.232 m. It would correspond to a fundamental of 739 Hz and a second harmonic of 1478 Hz. With respect to the various distortion peaks (510 Hz, 690 Hz, 870 Hz, 1050 Hz, i.e.. separated by about 180 Hz), I would suspect a non-linear component which could be transition of driver to enclosure.
 
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You can see from the measurements on page 1 that the distortion shows up in several peaks. The fundamental from top side of enclosure:

View attachment 237303
And second and third harmonics:
View attachment 237304

With respect to internal dimensions for calculating standing waves the inner distance between top and bottom is 0.232 m. It would correspond to a fundamental of 745 Hz and a second harmonic of 1478 Hz. With respect to the various distortion peaks (510 Hz, 690 Hz, 870 Hz, 1050 Hz, i.e.. separated by about 180 Hz), I would suspect a non-linear component which could be transition of driver to enclosure.
A little off topic, but …maybe all those resonances are small, compared to the out of phase sound coming from the inside of the box, and thru the drivers membrane.

 
I was mostly curious, especially about Thomas' results.

Your studies were very interesting I must say!:)

Speaking of resonances when it comes to subwoofers. It seems like a substantial braced box means that the resonance frequencies are pushed up in frequency and if you therefore use a steep LP filter, at least 24dB, at 80-100 Hz, you cut them off, and gets rid of those resonances.
No filling/stuffing is even needed in the subwoofer box. For the subwoofer that is. Full range speakers can definitely need filling/stuffing.

About this good braced::)

View attachment 237290

For frequencies below 100 Hz there are really no problems with respect to panel walls. Bracing not needed IMO.
 
For frequencies below 100 Hz there are really no problems with respect to panel walls. Bracing not needed IMO.
True with a cube formed subwoofer, not true If using 12dB/oct crossover or using a flat subwoofer box thats 1,5 meter long and made to be below a sofa or bench.

If the walls flex a little bit when playing music using a cube formed subwoofer, ( If using 12 mm mdf without bracing ) you will loose some dB output. So in practice - 18 mm plywood or a minimum 22 mm MDF is needed in a box thats 40*40*40 cm without bracing. 24 dB/oct crossover is to shallow for a single subwoofer in my opinion.
 
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True with a cube formed subwoofer, not true If using 12dB/oct crossover or using a flat subwoofer box thats 1,5 meter long and made to be below a sofa or bench.

If the walls flex a little bit when playing music using a cube formed subwoofer, ( If using 12 mm mdf without bracing ) you will loose some dB output. So in practice - 18 mm plywood or a minimum 22 mm MDF is needed in a box thats 40*40*40 cm without bracing. 24 dB/oct crossover is to shallow for a single subwoofer in my opinion.
I have subs that are 27x27x60 cm, 19 mm MDF, no bracing. What do you think the main modes will be? ;)
 
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