I was wondering if the energy that stuffing absorbs is done in a linear way vs power. What I mean is as a speaker is driven to louder output levels surely the energy the stuffing absorbs, becomes non-linear, perhaps by a "saturation" effect? By that, I mean as a percentage, it absorbs less energy as the volume increases? Would this be the reason that many speakers sound harsher as they are driven harder? I realise that drivers and amplifiers distort more as levels increase. If this is the case one would need to use sufficient stuffing to tune the speaker to the levels used at the chosen high loudness levels and perhaps accept slightly too much at quieter levels. One experiment would be to test the frequency response at the same power level with and without stuffing and then increase power to and see if any response changes could be observed when the levels on the plot had been corrected to overlay the first set. If less difference was observed between the with/without stuffing plots, this would reveal the reduced percentage absorption by the stuffing at high power levels.
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Thanks for your reply AllenB. You do say that there could be SOME change, so this small change might be audible? It makes me ask how great the change is. For all I know, the absorption could be greater when the speaker is driven louder and not necessarily less. I do agree that our hearing does work in a non- linear way and the 3kHZ area is so sensitive relatively to the rest of the spectrum. I would be interested in the way different stuffing materials might be more constant energy absorbers than others... However, maybe they all are the same in that regard, and their absorption profile remains substantially the same over a large range of acoustic energy levels? It must all be down to the fibres internal-frictional-losses and it makes me wonder that some might work very differently. I ask this question because I have never seen it mentioned, then again, maybe I have just missed the write ups.
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Interesting idea. I never gave it any thought before, but this how I view it.
The material's flow resistivity is measured as the pressure drop across the material for a given air flow rate (velocity). So if there is a change to resistivity, it must be caused by a change in the relative pressure drop for a given flow velocity. The density of the material effects the resistivity, and for box damping or absorption panels it's often spec'd as some amount of kg/m3 of fill. Pressure could cause the material to compress via Force = Pressure * Area and the resistivity would change (via density change). Fortunately, the pressure change (force) is an a.c. signal so the fibers would just oscillate with no net compression to change the material density so resistivity should not change.
I have not seen pressure as a variable in any absorption calculator, simulator or resistivity data spec. Still,.. I have no experiment or simulation result to actually prove that resistivity does not modulate (in some way) with pressure, but it seems unlikely from a thought experiment.
The material's flow resistivity is measured as the pressure drop across the material for a given air flow rate (velocity). So if there is a change to resistivity, it must be caused by a change in the relative pressure drop for a given flow velocity. The density of the material effects the resistivity, and for box damping or absorption panels it's often spec'd as some amount of kg/m3 of fill. Pressure could cause the material to compress via Force = Pressure * Area and the resistivity would change (via density change). Fortunately, the pressure change (force) is an a.c. signal so the fibers would just oscillate with no net compression to change the material density so resistivity should not change.
I have not seen pressure as a variable in any absorption calculator, simulator or resistivity data spec. Still,.. I have no experiment or simulation result to actually prove that resistivity does not modulate (in some way) with pressure, but it seems unlikely from a thought experiment.
As DonVK has also said, the effect in theory is linear with frequency.. That doesn't mean there isn't nonlinearity too. Nonlinearity exists in a great many things and in some things it doesn't matter to us and in some things there's not enough of it to matter to us. We are not as sensitive to nonlinear sounds as it seems based on what we suspect we hear is nonlinear.
I am curious. Perhaps the question here is whether there is a reduction in linear damping with level, or a nonlinear restoring pressure within the box?
Thanks DonVK... I always thought the stuffing worked by its ability to absorb sound energy and, through internal molecular friction, convert the absorbed sound wave modulation into heat? I never saw the stuffing as modifying any air flow through it. If it is, as I suggest, converting sound into heat energy, then at higher intensities the stuffing might heat slightly more, and its stiffness/viscosity will become lower and perhaps flex more easily with less energy absorption. This is just one way I see the "mechanics" of how it works and how there could be variations when subjected to different sound intensities. I agree the change due to heating is likely to very slight. Another way (perhaps even more likely?) that non linearities could be created is in the way the elastic nature of any fibres must be non-linear, just the same way as a spring deflects less under increased force as its bending forces oppose the bending pressure. I just can't help thinking that stuffing cannot work the same way at high volumes compared to low volumes. The experiment would be quite simple to do. I would use a sealed-type enclosure as not to introduce further complexities.
Yes, the air (and fiber) movement (kinetic energy) is converted to heat but the measurement of its resistance is using the pressure drop.
I have one other data point. Some time ago I was interested in cardiods and aperiodic vents but later abandoned the idea. However, I built an Acoustic Impedance Tube with Octave scripts to measure the impedances of acoustic filters with custom layers. There's an example at Ceiling Tile Measurement . I remember trying to find a good power level for the measurement, but since the measurement was relative, it turned out to not matter. However, I never tried the pressure levels you are probably considering, the mics would never tolerate it 🙂
I have one other data point. Some time ago I was interested in cardiods and aperiodic vents but later abandoned the idea. However, I built an Acoustic Impedance Tube with Octave scripts to measure the impedances of acoustic filters with custom layers. There's an example at Ceiling Tile Measurement . I remember trying to find a good power level for the measurement, but since the measurement was relative, it turned out to not matter. However, I never tried the pressure levels you are probably considering, the mics would never tolerate it 🙂
Hi Don. The levels I envisage are from quiet music to very loud .... something like from 50db to 90-100db levels a power ratio of 10,000 or 100,000: 1 (If my maths is correct?) As you can see, the power range is huge, so the energy absorption range has to be huge too. I have spent quite some time trying to find graphs of Sound Absorbtion vs Sound Intensity levels but surprisingly nothing comes up. Only sound absorption vs Frequencies.... but all at a constant level alas. However, this could indicate that different levels do not make any difference with any said absorption material 🥴 I'm still convinced there will be though🙂 SP: remember also that commercial sound absorption is not really concerned with how linear the reduction is...it just needs to reduce the sound, any sound, at any level....It does not matter if the reduction is non-linear....however with speakers I say it does
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Assuming that energy absorption is proportional to some function of speed and pressure, it can be noticed that a sine wave has twice as many speed peaks per cycle as velocity peaks, because minimum velocity is just maximum speed again but in the opposite direction. So the system is asymmetric and that immediately gives us a plausible mechanism for harmonics and IMD.
https://data-bass.com/systems/5bd0c4ea20120c00040a9bed
Josh Ricci has tested literally tons of subwoofers, other than the non-linear effects the speakers show due to excursion limitations, there do not seem to be any "saturation" effects that would be attributed to absorption non-linearity.
If you could tease any out, they would be inconsequential by comparison to the loudspeaker non-linearities, and transmission of interior reflected sound through the cone.
No, the distortion when driven past Xmax (10%) and impedance changes due to voice coil heating account for "harshness". The impedance can double (or more) at high drive levels, which can radically shift passive crossover points, while dropping the amplifier output by -3dB (or more).
Without damping material ("stuffing") resonance decay time will increase with SPL, which can change frequency response.
The levels inside the cabinet may be several orders of magnitude higher than outside.
In the chart above, levels of 110dB at two meters would equate to 116dB at one meter, interior SPL would be in the 160dB range.
Air actually becomes non-linear at those levels, but the response outside the subwoofer cabinet does not reflect that problem.
In high frequency horns, the diaphragm and throat SPL may go well into the non-linear range, and result in waveform distortion, though the frequency response stays relatively consistent with SPL increase.
Mics that can handle 170dB SPL without (much..) distortion are quite expensive.
This GRAS 47BG-FV has a dynamic range of 60dB(A) to 184dB, though does not list it's distortion level..
Test away!
Art
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Thank you so very much weltersys. I am bowled over by your superb set of replies. I thought it covered everything.... UNTILL I noticed the woofer responses were only up to just 100 Hz! The way I see it is that stuffing doesn't really do that much "absorption" at low frequencies, the shear energy, in effect, just steam rollers the materials around with very little effect on shaping the response *. It's my belief that wadding has a far greater impact in the mid frequencies causing the lightweight fibres to oscillate and generate heat thus absorbing energy. Low frequencies probably just move or shake the fibrous material en-mass, rather than get small fibres to vibrate. Saturation will not occur if the whole lump of fibre is moving in this way. So, as comprehensive a reply as you provide here, for me and my thinking, it misses the test on the mid-range response which is what I was asking about in my first question, and that is: "does stuffing absorb proportionally less energy at mid frequencies as loudness increases". Once this is done and shown whatever the result, I would have the full answer and be happy with it. * Note: I am not saying it does not have ANY effect.
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Try drawing some sine waves on paper, just as a thought experiment. One representing particle position, one shifted by 90° degrees for velocity, and another for acceleration (the inverse of position). Say that the regions with max and max negative velocity get positive pressure added. What happens to the shape of the wave?
Edit: actually, it may be possible to set up a test, sealing the end of a long tube with a transducer, stuffing the length of the tube, and measuring the output at the far end. For exaggerated effects, the tube could be a few metres long. Play a test signal, and see if any harmonics show up on the visual equipment. Listening may also be possible.
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The reason I suggest doing the test at both extremes With and Without stuffing, is that the speaker and the box enclosure itself will almost certainly have a different response at high levels anyway. Doing it with and without will enable the DIFFERENCES to be extracted from the low-level response, if any existed
I just can't get my head to work out what the result is "abstract".... I would be pleased to know the answer. especially in terms of sound absorption. Thanks
I was obviously referring to external sound levels at normal listening distance. Obviously, the inside levels will be higher but the range between the two quoted levels will be in the same order of magnitude
Hi Art,
The air-spring in a box is non-linear and different with in and out movements of the cone. Internally the air can be infinitely pressurized, but only rarefied to 0 psi. This may also cause some non-linearities of the adsorption properties of stuffing inside the box.
The air-spring behavior difference between in and out strokes also gives rise to some distortion. Linkwitz developed an Excel spreadsheet that makes an estimate of this contribution to the speaker's distortion based on the ratio of Sd*Xmax to Vbox.
I suppose similar nonlinearity with cabinet wall resonances. Low spl - no excitation, high spl would reach "Xmax" and compress
@sonicles There are a few more details that might help.
Usually, there is only interest in the porous material damping losses (R). The the losses depend on the material resistivity and the thickness. It is possible to absorb low freq with enough thickness. I have some references to material tables, a calculator and actual room measurements at Multilayer Absorber Panels . (a link is easier than repeating all of that 🙂 ).
Porous absorbers also have reactance that is never published because most users are only concerned with damping losses. The material contains air and has inertance (L) and the air is compressible (C) so it has reactance and can store energy. A more complete view of the absorber coefficients vs freq would be a table of complex numbers (R+jX) vs freq. An acoustic impedance tube can provide this table, but usually just the magnitude is published. The reactive part will only cause phase shift which might be useful for filters.
Usually, there is only interest in the porous material damping losses (R). The the losses depend on the material resistivity and the thickness. It is possible to absorb low freq with enough thickness. I have some references to material tables, a calculator and actual room measurements at Multilayer Absorber Panels . (a link is easier than repeating all of that 🙂 ).
Porous absorbers also have reactance that is never published because most users are only concerned with damping losses. The material contains air and has inertance (L) and the air is compressible (C) so it has reactance and can store energy. A more complete view of the absorber coefficients vs freq would be a table of complex numbers (R+jX) vs freq. An acoustic impedance tube can provide this table, but usually just the magnitude is published. The reactive part will only cause phase shift which might be useful for filters.