Unfortunately, thicker walls will raise resonance frequencies but do not reduce amplitude. This has been shown time and again in measurements. If anything, Q tends to increase as mass and stiffness go up.
Cabinet walls are essentially transparent at resonance. The only way to reduce sound transmission is with damping.
If a cabinet wall is stiff, heavy and lightly damped, for example something like a thick steel wall, will the deflection of the cabinet wall be large or small?
Given the steady state amplitude of an undamped resonance is infinite I am sure all will agree on the importance of damping. Is it easier to damp resonances at high frequencies, low frequencies or about the same?
Since SPL is fairly constant with frequency, we have to assume panel acceleration is constant, but that means displacement drops about 12 dB per Octave. What we need to remember about resonance is that mass reactances and stiffness reactances, by definition are cancelling each other out at resonance. It doesn't matter at all how stiff a cabinet is, or how massive it is. At resonance the two cancel and the cabinet is transparent unless damping is present.
Not sure about infinite amplitude, lets just say there is no mechanical impedance to resist motion. Good question about the frequency effectiveness of damping. Damping is generally prportional to velocity, which implies it might be more effective at lower frequencies, but I would want to run tests before proclaiming that.
David
Hello,
IMO the only cabinets which can avoid bending motion (bending waves) by pure stiffness are compact subwoofer cabinets.
Here we can push the resonances out of the used frequency range.
In almost all other cases we will have to live with resonances occuring within the used bandwidth.
Possible strategies
- let mass per area dominate stiffness and make the walls "mass hampered"
- segment the cabinet into segments of differing resonance and make the gaps between segments lossy (damping gaps)
- use dampening mats of high mass like e.g. polymer bitumen, to bring resonance frequencies and Q down.
My "credo":
In any enclosure not being a subwoofer, you cannot "fight" resonance by using solely "thickness" and "stiffness" of the walls.
Which in fact seem's to be close to what Dave already said above ...
There lies another danger in walls getting too stiff:
When you reach the coincidence frequency of the wall - that is bending waves od the wall propagate as fast as sound in air - then the cabinet begins to radiate unwanted sound very effectively.
What we want is a cabinet, that has low unwanted sound radiation: It is an advantage, to have bending waves propagate well below the speed of sound, if we cannot avoid them completely.
In this respect a stiff wall of low density is the most undesirable one ... but in a subwoofer you may use it consciously. Nevertheless a sufficiently low Q of the cabinet wall's resonances is always of advantage.
Pics 3 and 4 on my website below (bottom of page) show a bell mode of a small subwoofer cabinet occuring at about 220Hz. It is the lowest mode of that cabinet, so it can be operated without cabinet modes in the desired frequency range from 26Hz ... 80Hz
Schwingungen an Lautsprechergehusen
I used "durum wheat semolina" (Hartweizengrieß) to show the nodes of the bending wave modes, and i used lots of voice coil current ... "don't try this at home" without ensuring that VC is cooled suffiently.
Experts use a scanning Vibrometer (Laser Interferometer) to show those modes, but i am a "poor Expert" only ...
IMO the only cabinets which can avoid bending motion (bending waves) by pure stiffness are compact subwoofer cabinets.
Here we can push the resonances out of the used frequency range.
In almost all other cases we will have to live with resonances occuring within the used bandwidth.
Possible strategies
- let mass per area dominate stiffness and make the walls "mass hampered"
- segment the cabinet into segments of differing resonance and make the gaps between segments lossy (damping gaps)
- use dampening mats of high mass like e.g. polymer bitumen, to bring resonance frequencies and Q down.
My "credo":
In any enclosure not being a subwoofer, you cannot "fight" resonance by using solely "thickness" and "stiffness" of the walls.
Which in fact seem's to be close to what Dave already said above ...
There lies another danger in walls getting too stiff:
When you reach the coincidence frequency of the wall - that is bending waves od the wall propagate as fast as sound in air - then the cabinet begins to radiate unwanted sound very effectively.
What we want is a cabinet, that has low unwanted sound radiation: It is an advantage, to have bending waves propagate well below the speed of sound, if we cannot avoid them completely.
In this respect a stiff wall of low density is the most undesirable one ... but in a subwoofer you may use it consciously. Nevertheless a sufficiently low Q of the cabinet wall's resonances is always of advantage.
Pics 3 and 4 on my website below (bottom of page) show a bell mode of a small subwoofer cabinet occuring at about 220Hz. It is the lowest mode of that cabinet, so it can be operated without cabinet modes in the desired frequency range from 26Hz ... 80Hz
Schwingungen an Lautsprechergehusen
I used "durum wheat semolina" (Hartweizengrieß) to show the nodes of the bending wave modes, and i used lots of voice coil current ... "don't try this at home" without ensuring that VC is cooled suffiently.
Experts use a scanning Vibrometer (Laser Interferometer) to show those modes, but i am a "poor Expert" only ...
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Why assume acceleration is constant? What would seem to be constant is something related to the motion of the driver.
Will a driver bolted to a thick metal cabinet being driven at the resonant frequency immediately cause large deflections in the cabinet because the forces due to mass and stiffness are of equal magnitude but opposite sign? Would a thin metal cabinet behave in the same way?
If the frequency is very close but not exactly at resonance (to avoid division by zero), or perhaps at resonance but with a tiny and equal amount of damping, will the thick and thin metal cabinets deflect the same amount?
If the damping force is proportional to velocity wouldn't it be larger at higher frequencies and not lower frequencies?
David, we have to thank you for making this clear. Even if it should be necessary to make this clear over and over again ...
Humans seem to "trust" intuitively in thick and stiff walls. But those are not always helpful when it comes to structure born sound ...
Mass and damping usually is needed to reduce structure born sound from walls while too much stiffness can be counterproductive.
Yes, it is a fundamental audiophile belief that thicker and stiffer Cabinet walls "must be better". People should take a look at the work done to earthquake proof buildings. Increasing building stiffness would be unrealistic but large seismic masses in vats of oil (i.e. damping) are quite useful.
As to showing panel vibration with powders, here is a Cool video.
http://www.youtube.com/watch?v=wvJAgrUBF4w&feature=youtube_gdata_player
Regards,
David
Diaphragms of any kind radiating wavelengths much longer than their dimension require constant acceleration for flat SPL. The same would be true of a cabinet wall.
If acceleration is constant then velocity rises at low frequency and displacement rises with the square of downward shift.
David
Thanks for explaining where you are coming from which was baffling me a bit. I understand what you are saying about simple sources at low frequencies but I need to think further about how applicable it is to our cabinets and it is getting late here. I shall have a ponder tomorrow evening.
I can only speculate that some of you people must be failed politicians;failed in as much as that if you had paid attention you would know that you ALWAYS preface the answer to a question that you don't want to or can't answer with "I'm glad you asked me that because . . ."
ps - have a wonderful Easter
ps - have a wonderful Easter
("Käse" german for "cheese" may be translated similar to "bull****", when used
to comment a statement)
Dear member "ticktock",
you are showing to us plumply that your knowledge in acoustics and structure born sound is void.
This is not an unusual behaviour at all in most internet forums on audio equipment.
Nevertheless it has been - up to now - an unusual manner in this particular forum to debase someones knowledge and statements, especially if the person is a highly recognized researcher and designing engineer in the field of electroacoustics.
This forum can be proud of having recognised members, willing to share their knowledge and also giving practical advice.
Unfortunately there are also members behaving like you, pulling social graces and knowledge transfer down in an intolerable way.
I hope sincerely, that such kind of behaviour will be repelled consequently, and i am willing to contribute my share to do that:
There are lot's of forums in german language, where users with void knowldege and bad manners are welcome.
I will be glad to give you some hint's to those forums if needed ...
Kind Regards
Oliver
For a typical cabinet with a dimension of around a foot and resonances beginning at a few hundred Hertz this assumption does not seem to hold. The product of wavenumber and cabinet dimension is likely to be greater than 1 for the first mode and rising for the higher modes. It will be tending towards constant velocity not constant acceleration as the radiation increasingly beams. However the motion of the cabinet is no longer that of a simple piston and so a bit more pondering may be required to have confidence in how things are likely to scale.
Can you provide a reference to check we are not at cross purposes.
A thick wall is normally stiffer than a thin wall. In the expression for the deflection of a forced mass-spring-damper system compliance appears in the numerator. So a thick wall can be expected to deflect less than a thin wall when subject to the same forcing by the driver and the same amount of damping.
So stiff cabinets are going to be quieter than less stiff ones unless whatever is stiffening the cabinet reduces the damping by more than the stiffness is increased. So what changes the effectiveness of the damping?
Andy,
in my view, what David wrote is true when thinking of pistonic acting diaphragms which have dimensions small compared to wavelength.
What is essentially constant throughout the upper bass and midrange - as the main frequency ranges of interest here - is the driving force.
The driving force acting upon the diaphragm also acts upon the baffle of the cabinet.
You are right in that the cabinet will not move like a lumped mass but will exhibit bending modes. In a typical structure able to exhibit such modes it will be the average velocity (averaged over the whole surface area of the cabinet) , which is constant over frequency.
So usually -e.g. in a bending wave transducer's diaphragm - radiated sound energy tends to be constant over frequency [1].
There is one effect, causing the efficiency of sound radiation to rise with frequnency: That is the propagation speed of bending waves being dispersive [2].
If you move up in frequency, the bending waves will propagate faster up to a point where bending waves propagate as fast as sound in air.
This is the so called coincidence frequency Fc. Near and especially above Fc the efficiency of radiation increases dramatically, even though the average velocity of the structure (cabinet walls) still keeps approximately constant.
This is one main reason to avoid cabinet resonances being too high in frequency and too high in Q.
The cabinet radiation above Fc will also exhibit lobes, which makes those radiation audible if such a (cabinet!) radiation lobe is accidentally directed at the listener's seat.
Cheers
____________
[1] Given the modal overlap factor is high e.g. >3
The modal overlap in a vibrating speaker cabinet ist usually low at the lowest modes, so in fact we have velocity maxima at the lowest resonances causing also maxima of sound radiation from the cabinet at those lowest modes.
When frequency rises also modal overlap rises and the radiation will be more constant over frequency, at least as long as F << Fc.
[2] We have to make a strict distinction between "velocity of the walls" in terms of vibration and the "propagation speed" of the waves: The latter is rising with frequency because bending waves on a structure are dispersive. Sound progagation in air is not dispersive but has constant - frequency independent - speed of propagation.
in my view, what David wrote is true when thinking of pistonic acting diaphragms which have dimensions small compared to wavelength.
What is essentially constant throughout the upper bass and midrange - as the main frequency ranges of interest here - is the driving force.
The driving force acting upon the diaphragm also acts upon the baffle of the cabinet.
You are right in that the cabinet will not move like a lumped mass but will exhibit bending modes. In a typical structure able to exhibit such modes it will be the average velocity (averaged over the whole surface area of the cabinet) , which is constant over frequency.
So usually -e.g. in a bending wave transducer's diaphragm - radiated sound energy tends to be constant over frequency [1].
There is one effect, causing the efficiency of sound radiation to rise with frequnency: That is the propagation speed of bending waves being dispersive [2].
If you move up in frequency, the bending waves will propagate faster up to a point where bending waves propagate as fast as sound in air.
This is the so called coincidence frequency Fc. Near and especially above Fc the efficiency of radiation increases dramatically, even though the average velocity of the structure (cabinet walls) still keeps approximately constant.
This is one main reason to avoid cabinet resonances being too high in frequency and too high in Q.
The cabinet radiation above Fc will also exhibit lobes, which makes those radiation audible if such a (cabinet!) radiation lobe is accidentally directed at the listener's seat.
Cheers
____________
[1] Given the modal overlap factor is high e.g. >3
The modal overlap in a vibrating speaker cabinet ist usually low at the lowest modes, so in fact we have velocity maxima at the lowest resonances causing also maxima of sound radiation from the cabinet at those lowest modes.
When frequency rises also modal overlap rises and the radiation will be more constant over frequency, at least as long as F << Fc.
[2] We have to make a strict distinction between "velocity of the walls" in terms of vibration and the "propagation speed" of the waves: The latter is rising with frequency because bending waves on a structure are dispersive. Sound progagation in air is not dispersive but has constant - frequency independent - speed of propagation.
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Just a remark:
When increasing a wall's thickness by using the same material - e.g. by "doubling" - stiffness will increase noteably more than "mass per area" which causes
- resonant modes of same order number to increase in frequency
- lowering of the coincidence frequency Fc of the walls, because the propagation speed of bending waves rising.
"Bracing only" is going into the same direction, but even more extreme, because bracing does not increase the "mass per area" in the same way:
- walls get even more "stiff and lightweight"
- Fc drops even further and may even be lowered to lower midrange or even upper bass (!) instead of staying in the upper midrange or treble region, where it ideally belongs e.g. in a 2 way speaker cabinet. ...
Lowering Fc makes unwanted and resonant sound radiation from the cabinet more effective in the midrange.
Again: "Increasing stiffness by increased thickness and/or bracing of the walls soleley" is not a way to go for making wideband loudspeaker cabinets, which are going to be used from lower bass to upper bass and possibly also midrange.
That strategy may only be practical when properly controled my measurement to make subwoofer cabinets having structural resonances well above the used bandwidth.
I know, there are (and will be) lot's of DIYers and also professional designers who won't believe and will not understand those basic facts even within that short timespan called "future" which mankind still has to expect on this panet.
That's why we will still have to cut more wood than necessary to build louspeaker's cabinets and having acoustically bad cabinets at the same time.
"LineArray said:
When increasing a wall's thickness by using the same material - e.g. by "doubling" - stiffness will increase noteably more than "mass per area" which causes
- resonant modes of same order number to increase in frequency
- lowering of the coincidence frequency Fc of the walls, because the propagation speed of bending waves rising.
"Bracing only" is going into the same direction, but even more extreme, because bracing does not increase the "mass per area" in the same way:
- walls get even more "stiff and lightweight"
- Fc drops even further and may even be lowered to lower midrange or even upper bass (!) instead of staying in the upper midrange or treble region, where it ideally belongs e.g. in a 2 way speaker cabinet. ...
Lowering Fc makes unwanted and resonant sound radiation from the cabinet more effective in the midrange.
Again: "Increasing stiffness by increased thickness and/or bracing of the walls soleley" is not a way to go for making wideband loudspeaker cabinets, which are going to be used from lower bass to upper bass and possibly also midrange.
That strategy may only be practical when properly controled my measurement to make subwoofer cabinets having structural resonances well above the used bandwidth.
I know, there are (and will be) lot's of DIYers and also professional designers who won't believe and will not understand those basic facts even within that short timespan called "future" which mankind still has to expect on this panet.
That's why we will still have to cut more wood than necessary to build louspeaker's cabinets and having acoustically bad cabinets at the same time.
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Always a lively discussion when we get into cabinet theory!
Andy raises some good points and it is true that at higher frequencies a cabinet may get "above the corner" in terms of ka number and not be simply in the "flat acceleration = flat response" region. Clearly the higher cabinet modes are highly complex and both output and polar response of cabinet radiation are matters that we should only generalize carefully about.
The whole mass and stiffness thing defies logic at first blush. I like to view it the way architectural acoustics people do. If I have noisy neighbors then I want walls with high transmission loss or TL. The best parameter for noise isolation is barrier mass. Acousticians refer to an ideal of the "limp mass barrier". That is think of making walls with heavy rubber sheet. You can make them thicker and they will become heavier, but because we have found some ideal limp material they will remain resonance free. It turns out that such a limp mass gives a transmission loss that climbs 6dB per Octave (every Octave we go up it becomes 6dB more effective as a barrier) and I can also raise the whole curve by doubling the mass per square foot, for a 6dB improvement.
Unfortunately my barrier is poor at DC and will have no isolation. I can add stiffness to give low frequency isolation and every time I double stiffness I will double my low frequency isolation.
This sounds great--combine high mass with high stiffness--but I have now created a resonant system. At some frequency the positive reactance of mass and the negative reactance of stiffness are equal in amount and opposite in phase. At that frequency we will have ZERO transmission loss or all the sound will get through (see attached Barlow curves). The only possible barrier to sound transmission is if there is loss in the system: i.e. damping material.
Here is a good web site that goes into the basics of wall construction with regard to transmission loss.
Noise insulation case
It give graphs for mass loss and shows some of the resonances that occur in walls and how they effect TL. Note that this is a curve of loss and higher up the scale is good. The bottom of the scale represents unwanted wall transparency.
Should we compare rooms to cabinets? (note, Cabinet = small cabin or room).
Wall transmission just looks at the simple case of one wall of our room. Speaker cabinets are fairly complex beasts with multiple resonances for each of the 6 sides and also complex coupling from one wall to the other via the edge joints. Still, the basics of mass and stiffness and damping and resonances all apply. Adding mass will move resonances down, adding stiffness will move resonances up, and at resonance we rely on damping to prevent total sound transmission.
I cite Harwood a lot because he wrote a very practical paper that is exactly on point. Below is a pair of graphs where he made a standard undamped cabinet and measured the wall output. He then doubled the wall thickness and made the same measurements. As you would expect the cabinet resonances went up in frequency. They are very nearly the same SPL at their higher frequencies. As he had earlier determined that our threshold of audibility was falling through this range (we could detect resonances at lower level: we were more sensitive to resonances) then this made those particular resonances more audible.
Oops.
Barlow did a similar study but he put a loudspeaker and cabinet within another cabinet. That is, he buried a speaker so that it should have been totally silenced except for any sound that could seep through the outer cabinet.
He found that there was one major frequency where the sound was nearly as loud as if there were no outer cabinet. When he used thicker and thicker cabinets the frequency of resonance went up but it did not change in level.
These two sets of graphs are what I base the claim on, that cabinet output is constant even though stiffer walls have pushed resonances up.
Thicker cabinet walls doeth not a better cabinet make.
LineArray is correct that a subwoofer is a special case where we might push the resonance up an Octave and get them totally out of the band of operation. Not so for 2 and 3 way cabinets. In general, doubling wall thickness will double wall mass and give 8 times the beam stiffness for a given wall. In very broad terms we can expect resonances to go up one Octave. (square root of stiffness over mass or 8 over 2). How much do you think you can raise resonances? How high do they need to go to be inaudible?
Regards,
David
Andy raises some good points and it is true that at higher frequencies a cabinet may get "above the corner" in terms of ka number and not be simply in the "flat acceleration = flat response" region. Clearly the higher cabinet modes are highly complex and both output and polar response of cabinet radiation are matters that we should only generalize carefully about.
The whole mass and stiffness thing defies logic at first blush. I like to view it the way architectural acoustics people do. If I have noisy neighbors then I want walls with high transmission loss or TL. The best parameter for noise isolation is barrier mass. Acousticians refer to an ideal of the "limp mass barrier". That is think of making walls with heavy rubber sheet. You can make them thicker and they will become heavier, but because we have found some ideal limp material they will remain resonance free. It turns out that such a limp mass gives a transmission loss that climbs 6dB per Octave (every Octave we go up it becomes 6dB more effective as a barrier) and I can also raise the whole curve by doubling the mass per square foot, for a 6dB improvement.
Unfortunately my barrier is poor at DC and will have no isolation. I can add stiffness to give low frequency isolation and every time I double stiffness I will double my low frequency isolation.
This sounds great--combine high mass with high stiffness--but I have now created a resonant system. At some frequency the positive reactance of mass and the negative reactance of stiffness are equal in amount and opposite in phase. At that frequency we will have ZERO transmission loss or all the sound will get through (see attached Barlow curves). The only possible barrier to sound transmission is if there is loss in the system: i.e. damping material.
Here is a good web site that goes into the basics of wall construction with regard to transmission loss.
Noise insulation case
It give graphs for mass loss and shows some of the resonances that occur in walls and how they effect TL. Note that this is a curve of loss and higher up the scale is good. The bottom of the scale represents unwanted wall transparency.
Should we compare rooms to cabinets? (note, Cabinet = small cabin or room).
Wall transmission just looks at the simple case of one wall of our room. Speaker cabinets are fairly complex beasts with multiple resonances for each of the 6 sides and also complex coupling from one wall to the other via the edge joints. Still, the basics of mass and stiffness and damping and resonances all apply. Adding mass will move resonances down, adding stiffness will move resonances up, and at resonance we rely on damping to prevent total sound transmission.
I cite Harwood a lot because he wrote a very practical paper that is exactly on point. Below is a pair of graphs where he made a standard undamped cabinet and measured the wall output. He then doubled the wall thickness and made the same measurements. As you would expect the cabinet resonances went up in frequency. They are very nearly the same SPL at their higher frequencies. As he had earlier determined that our threshold of audibility was falling through this range (we could detect resonances at lower level: we were more sensitive to resonances) then this made those particular resonances more audible.
Oops.
Barlow did a similar study but he put a loudspeaker and cabinet within another cabinet. That is, he buried a speaker so that it should have been totally silenced except for any sound that could seep through the outer cabinet.
He found that there was one major frequency where the sound was nearly as loud as if there were no outer cabinet. When he used thicker and thicker cabinets the frequency of resonance went up but it did not change in level.
These two sets of graphs are what I base the claim on, that cabinet output is constant even though stiffer walls have pushed resonances up.
Thicker cabinet walls doeth not a better cabinet make.
LineArray is correct that a subwoofer is a special case where we might push the resonance up an Octave and get them totally out of the band of operation. Not so for 2 and 3 way cabinets. In general, doubling wall thickness will double wall mass and give 8 times the beam stiffness for a given wall. In very broad terms we can expect resonances to go up one Octave. (square root of stiffness over mass or 8 over 2). How much do you think you can raise resonances? How high do they need to go to be inaudible?
Regards,
David
Attachments
Speaker Dave said:
Well structured post and a pleasure to read, just a comment on subwoofer's and midranger's cabinets:
Like in a subwoofer one may think of "pushing resonances out of the used bandwidth" towards higher frequencies one could think the other way round when it comes to cabinets used from midrange upwards only:
Then a "massive rubber like" floppy structure having very low stiffness (but mass and damping) seems practical as a cabinet.
Seen in this way a mutliway design is not only an option to use transducers which are well chosen for their particular frequency range, but to to the same with the cabinets e.g.:
- ultra stiff walls (but somewhat damped) for the subwoofer.
- "floppy but massive and highly damped" walls for upper bass and midrange
Such a midrange cabinet could be made large enough, so that compliance of the air enclosed is very high compared to the drivers compliance.
A large mass located at the driver's motor would "mass hamper" excitation of the baffle via the driver's basket.
After reading your posts, I think I get it.
You push the resonant frequencies up so that the woofer can't excite them.
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