My main problem is that someone makes its reasonings in terms of (apparent) density and other in terms of porosity (that in turn requires the knowledge of the bulk density). I shall work on that.
For the moment let me assume that Tarnow and Robinson agree (at least on that).
14 kg/m3 would mean 3276 rayls/m. This is a flow resistance one order of magnitude higher than the flow resistivity used by MJK in his TL (and by me in mine).
As you (and anybody willing to) can see, the difference among the "moving fiber" model and the "rigid fiber" model gets smaller as the density gets smaller (who puts 30 kg/m3 of fiberglass in his loudspeakers ?).
On the contrary in the Robinson's thesis you can see resonances already at 2.6 kg/m3.
Do you understand why I' becoming crazy ?
For the moment let me assume that Tarnow and Robinson agree (at least on that).
14 kg/m3 would mean 3276 rayls/m. This is a flow resistance one order of magnitude higher than the flow resistivity used by MJK in his TL (and by me in mine).
As you (and anybody willing to) can see, the difference among the "moving fiber" model and the "rigid fiber" model gets smaller as the density gets smaller (who puts 30 kg/m3 of fiberglass in his loudspeakers ?).
On the contrary in the Robinson's thesis you can see resonances already at 2.6 kg/m3.
Do you understand why I' becoming crazy ?
I would think the difference between the "moving fiber" model and the "rigid fiber" model should become smaller as density gets larger due to the fact the the fibers are more structurally supported by the neighboring fibers.
Ahh, thinking about it a bit more, if the fiber matt is placed against a wall, then it may be possible that difference between the "moving fiber" model and the "rigid fiber" model become smaller as density gets smaller.
Ahh, thinking about it a bit more, if the fiber matt is placed against a wall, then it may be possible that difference between the "moving fiber" model and the "rigid fiber" model become smaller as density gets smaller.
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The fiber against a wall model should work for enclosed loudspeakers, no?
It's my experience 14-18 kg/cu. m is typical for FG in an enclosed box. IIRC, King's site recommends something on the order of 8 kg/cu.m for TL's as a starting point with recommendations to experiment around that amount to optimize the attenuation of post resonance ripples in the response.
Please forget about the distinction "fiber agaist a wall" and "fiber in a tube" and "fiber in a closed box".
These are three different aspects of the same physical quantities: the effective impedance and effective speed of sound (complex quantities) (or, and this is the same, effective density and effective bulk modulus) of the equivalent fluid.
These are three different aspects of the same physical quantities: the effective impedance and effective speed of sound (complex quantities) (or, and this is the same, effective density and effective bulk modulus) of the equivalent fluid.
True. If a model can be developed to predict fiber effects on damping more accurately, that would be a breakthough. However, we must take into account the velocity profile and the direction of the fibers. Fibers that run parallel with the velocity vector will provide less frction than when perpendicular to the velocity vector. Depending on wavelength/material thickness, whether against wall or not effects the velocity profile in the fiber material, and thus changes the damping characteristics. I have not gone through the math of these papers in detail yet, but my initial guess based on experience in reviewing various documents and reports, the velocity profile variation in the fiber material and the fiber direction probably were not taken into account during modeling.
Ah, on the APMR site, I found this:
Choosing a suitable model
First, it is obvious that in case of mechanical excitation of the medium, the motionless skeleton models can not be used. Depending of the frequency range studied, a diphasic or a uniform pressure model can be used.
At low frequencies, when the wavelength is very much larger than the thickness of the material sample, a uniform pressure approximation inside the sample can be considered. At higher frequencies, a diphasic model must be used.
At very low frequencies when the wavelength λ is very much larger than the thickness h of a porous material sample, the pressure values on both sides of the sample: p2 and p1 can be considered as equivalent. A uniform pressure field is thus assumed in the sample and a "equivalent solid" model can be used to describe the acoustical behavior of the material.
In case of acoustical excitations, at low frequencies, waves can propagate in both phases and a diphasic model is required. Above a phase decoupling frequency [ZK49] a motion of the fluid phase does no more induce a motion of the solid phase. A Motionless skeleton model can thus be used to describe the acoustical behavior of the material.
Ah, on the APMR site, I found this:
Choosing a suitable model
First, it is obvious that in case of mechanical excitation of the medium, the motionless skeleton models can not be used. Depending of the frequency range studied, a diphasic or a uniform pressure model can be used.
At low frequencies, when the wavelength is very much larger than the thickness of the material sample, a uniform pressure approximation inside the sample can be considered. At higher frequencies, a diphasic model must be used.
At very low frequencies when the wavelength λ is very much larger than the thickness h of a porous material sample, the pressure values on both sides of the sample: p2 and p1 can be considered as equivalent. A uniform pressure field is thus assumed in the sample and a "equivalent solid" model can be used to describe the acoustical behavior of the material.
In case of acoustical excitations, at low frequencies, waves can propagate in both phases and a diphasic model is required. Above a phase decoupling frequency [ZK49] a motion of the fluid phase does no more induce a motion of the solid phase. A Motionless skeleton model can thus be used to describe the acoustical behavior of the material.
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Interesting point, I was not aware ot the notion of "decoupling frequency".
However they contributes to my crazyness: for the same (apparent) density, the higher is the flow resistivity the higher is the decoupling frequency.
So I would expect fiber movement on polyester when fiberglass doesn't move yet.
However they contributes to my crazyness: for the same (apparent) density, the higher is the flow resistivity the higher is the decoupling frequency.
So I would expect fiber movement on polyester when fiberglass doesn't move yet.
Look at those:
http://arxiv.org/ftp/arxiv/papers/0810/0810.3126.pdf
http://hal.archives-ouvertes.fr/docs/00/32/35/36/PDF/2007_doutres_a1.pdf
They are on the track I was following: "limp model".
Dealing with the full Biot Model is so difficult !
http://arxiv.org/ftp/arxiv/papers/0810/0810.3126.pdf
http://hal.archives-ouvertes.fr/docs/00/32/35/36/PDF/2007_doutres_a1.pdf
They are on the track I was following: "limp model".
Dealing with the full Biot Model is so difficult !
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