Sound Speed In Porous Absorbers

[avare]

In this thread amongst other things;

Originally Posted by prairiedog

I'm really not an expert in this area but if you're interested in what's happening inside a porous absorber, you probably need to take into account the fact that the speed of sound is less than that it is in air. This has two significant effects. Firstly, the wavelength is reduced. Secondly, the angle of incidence is reduced. I'm not going to quantify these effects but I would expect them to be important if you're trying to locate maximum particle velocity inside a porous absorber. Perhaps someone else can throw some light on this subject?

Great points Demetris. I find amazing how ignorant people here are of the speed of sound adiabatically versus isothermally. One of the most famous examples of the evolution of physics is Newton's misunderstanding of this and calculating the speed of sound from first principles. His error was using an isothermal model instead of adiabatic. Knowledge that is 4 centuries old.

In addition to the skewing of the angle of progression in the porous material, Snell's Law also comes into effect at the appropriate angles.

If acoustics was simple, god would not have created aspirin.

Andre

[prairiedog]

Great idea for a thread. This is something I'd like to learn more about.

I've done some reading and have discovered some things which I find very surprising. Perhaps I've misunderstood something. Either way, I would appreciate comments from Andre and/or other experts on this forum.

As I understand it, the speed of sound in air at room temperature is around 344 m/s. This is under adiabatic conditions. Inside a porous absorber at low frequencies, conditions are isothermal. This should result in a speed of sound which is lower by a factor of approximately 1.18 if no other factors come into play. This would give a speed of about 291 m/s.

To find out whether there are other factors to be considered I had a look through some papers and books and discovered the following:

According to Delany and Bazley (and others), the speed of sound in a porous absorber is given by the angular frequency divided by the real part of the complex wavenumber. If we take a porous absorber with flow resistivity 10,000 rayls/m, at a frequency of 100Hz the Allard/Champoux model predicts that the real part of the complex wavenumber will be 5.65 . Other models (eg. Miki, Delany/Bazley) give values in the same ballpark. If we divide the angular frequency (628.3) by 5.65 we should get the speed of sound in the porous absorber. This calculation gives us a value of 111 m/s. This is dramatically less than I expected, and if correct, has some interesting repercussions.

It has been shown that if the thickness of a porous absorber is at least 7% of the wavelength (in air), then we can get close to 100% absorption. Some people have found it difficult to believe that an absorber that thin can be so effective. If my calculations above are correct, then the wavelength inside the absorber is much shorter due to the reduced speed of sound. For a porous absorber with flow resistivity 10,000 rayls/m, at a frequency of 100Hz, 7% of the wavelength in air corresponds to about 22% of the wavelength inside the absorber. Very close to the 25% that many people feel is necessary for full absorption!

Any comments are welcome.

Demetris

[DanDan]

Thank you Demetris. That makes perfect sense.
DD

[Brainchild]

Very interesting. I'd be interested to know more, too, particularly about what the mechanisms are that lead to the further slowing of the wave; frictional, viscous losses, etc. It's also interesting to see the relationship to the refractive index of a material in the case of optical waves.

[avare]

Originally Posted by prairiedog

Great idea for a thread. This is something I'd like to learn more about.

I've done some reading and have discovered some things which I find very surprising. Perhaps I've misunderstood something. Either way, I would appreciate comments from Andre and/or other experts on this forum.

Thank you Demetris, your post is wonderful, and correct. We have tried in the past to get this point across, with minimal success. See the Q4 for Avare thread for details on that. We will develop this further, thanks to your post and the reminder of Delany and Bazley.

Brainchild, the starting point on bringing this physics to common knowledge, at least on Geekslutz, is the work of Delany and Bazley. I am looking forward to your research on this subject eagerly.

Andre

[Dange]

I put some impedance tube measured data up a while ago - http://www.gearslutz.com/board/5901624-post77.html



7% of the wavelength of 126Hz is 190mm in air

0.07*(343/126)=0.191 m = 190 mm

[Dange]

Thoughts out loud.....

In a closed tube with rigid termination, a standing wave will setup at a particular frequency where the incident and reflected waves meet. The frequency at which this occurs is set by geometry, distance from source to rigid termination. The area of highest velocity will be 1/4 wavelength from termination.

If you the add an absorber that is 7% of the wavelength and this drops the speed of sound to 111m/s. Then that's effectively changing the tube length, lengthening it? So the area of highest velocity will no longer be at 1/4 wavelength from termination, as the incident and reflected wave have 'travelled further'.........?

I'm not sure how accurate Delany and Bazley are at low frequency to make the speed of sound assumptions. But my above posted data ties in with the 7% depth

[localhost127]

Dange,

i was reviewing this thread and thinking along the same lines.

wouldn't a standing wave in a bounded space be modified slightly when a porous absorber is placed? (eg, if covering the entire modal surfaces)? or is it too insignificant to matter since the modal frequencys' wavelengths are so inherently long to begin with?

does placing large porous absorbers help off-set the mode by having the reflected wave be slightly out of sync/phase with the direct signal (since it had to travel through the porous absorber of which speed of sound is different)? does the porous LF absorber help minimize interference via absorption and also by slightly altering the phase of the reflected signal??

[avare]

Sorry I missed this earlier.

Originally Posted by Dange

If you the add an absorber that is 7% of the wavelength and this drops the speed of sound to 111m/s. Then that's effectively changing the tube length, lengthening it? So the area of highest velocity will no longer be at 1/4 wavelength from termination, as the incident and reflected wave

Close, ever so close. The 7% wavelength is of sound traveling in air. In the example you are using, with the speed of sound being one third that of air, the wavelength that sound sees is three times longer, which is 21% of the wavelength.

BINGO! The relationship between porous absorber depth and low frequency cut off according to the quarter wavelength theory is explained. As I have written for quite a while now, practical porous absorbers are not thin, as used in the quarter wavelength example of thin material and maximum particle velocity. When the speed of sound in the porous material is taken into account, the low end cutoff becomes significantly lower than the simplified example suggests. This also helps explain why the "optimum depth" folks thinking is flawed, because the material is acoustically significantly thicker than it is physically.

Andre

[boggy]

Originally Posted by avare

...... This also helps explain why the "optimum depth" folks thinking is flawed, because the material is acoustically significantly thicker than it is physically.

Andre

I agree, so because this, room become "larger" than physically is.

Couple of phenomenons that originate from this, may be:

- If we measure electrical impedance of loudspeaker driver in the closed box, before and after inserting rockwool in the box, we will see lowering Q of resonance, but also resonant frequency shift (easily noticeable) to the lower values, similar as we increase size of the box (we don't only see lowering Q because absorption). We may assyme that room is resonant cavity, similar to (closed) loudspeaker box, only (much) bigger.... so, if we place porous absorbers in the room, we acoustically increase size of the room alongside with resonances damping.

- Also we can see that different absorbing materials have different "cut-off" frequencies for same material thickness.. In this thread: My Experiment with a Metal Panel Absorber, I attached interesting graph where we can see points when absorption coefficient drop to 0.5, or something like "cut-off frequency" for absorbers, to region where they can't absorb significantly.There may be easily visible that different materials has this frequency different even if thickness of material is the same. This wouldn't be the case if only "optimum depth" variable figure in equation... Graph is built (in hurry) from available manufacturer informations, and some rough interapolation is applied to find f(0.5)...

Here it is again... with IsoBond included



Sorry, i didn't include flow resistivity in graph data...

[avare]

Boggy:

Thank you for a great post adding constructive data to the subject matter.

Constructively, and well constructed,
Andre

[kasmira]

Originally Posted by boggy

so, if we place porous absorbers in the room, we acoustically increase size of the room

Is this because when you add a panel into the room, it slows the speed of sound when it hits the absorption, making it seem like there's actually a hole in the wall at that point, increasing room size?

I'm still trying to understand just the basics of whats even going on in this thread. Hope no one minds if I ask lamens terms questions in here..

[boggy]

Andre, you are welcome!

Originally Posted by kasmira

Is this because when you add a panel into the room, it slows the speed of sound when it hits the absorption, making it seem like there's actually a hole in the wall at that point, increasing room size?

Some explaination may be... if we have same resonant cavity filled with air and filled with fluffy rockwool, we will have resonances at different frequencies. If we have partially filled cavity with porous absorber, resonant frequencies will be (slightly) lower than in an empty room (but filled with air!), or some value between (fully) air filled and room (fully) filled with porous absorber...

Originally Posted by kasmira

I'm still trying to understand just the basics of whats even going on in this thread. Hope no one minds if I ask lamens terms questions in here..

Try to understand that frequencies of room modes aren't defined only by dimensions of resonant cavity (room), but also by matter used to "fill" this cavity (air, porous absorber, partially absorber/air, ............ water will be different too,... etc.). If you accept this... then you can easily accept that room mode frequencies may not be exactly the same after significant treatment with porous absorbers (30-40% of room volume, for example)

So if we "remove" air from room in some regions, and put porous absorbers there, we will change frequencies of room modes (slightly), because boundaries conditions aren't the same as before... so we can conclude our treated room will behave as if it were a slightly bigger, we can't ignore influence of porous abosrbers anymore, regarding to modal frequencies.

This is easier to measure in closed box loudspeaker, when you measure electrical impedance of driver... this way it may be easier to notice.