Speed of Sound in Fibre

[DanDan]

On a long slow journey of discovering/learning Acoustics I have come across a 'consensus' that broadly speaking sound slows down about 20% when travelling through our typical fibres. Then, surprisingly, I came across some rather mathematical posts which suggest that down at (from memory, approximations) down around 50Hz sound travels at about 80 m/s.
A big gobsmacked, I have been wondering if this is literally the case?
If so, for spaces with deep fibre treatments, does it make Mode Calculators somewhat moot?
Put another way, are fibrous traps acoustically about 4 times deeper than they look?

[DanDan]

No takers? Here's the very slow speed proposal/theory/ https://www.gearslutz.com/board/bass-tr ... rbers.html

[Soundman2020]

Hey Dan. Yes, sound does slow down in fibrous insulation (that's part of the whole adiabatic / isothermal thing). It's also the reason why some explanations say that sound has a "longer path to travel" through insulation: only partly true, of course, but if it helps to think that slower speed = longer journey to make sense of it, I guess that's fine. I had never really gone into the math in detail, but I had always assumed the difference would be 1.414 (the square root of two) since that factor comes up in many equations. I may be wrong on that; it was just an assumption on my part, without checking (and assumptions without checking are rather dumb! But anyway...). That would make for 69% of free-air speed inside the insulation, so roughly 240 m/s (31% reduction), which differs quite a bit from the figure you mentioned! I'll take a look at that thread to see where that 80 m/s figure comes from: I never thought it would be that low!

- Stuart -

[Soundman2020]

OK, I took a look at the thread, and it pretty much ties in with what I expected... except that the actual reduction factor seems to be up in the air still! Andre says "21%" but also "one third", you mentioned 77%, I figured 31%, but your really cool experiment shows a real-word reduction of about 37%. Maybe you could try that with different types of insulation, and with deeper and shallower depths, to confirm? Is it possible that your mic position changed slightly between tests, which could be why you show 37% instead of Andre's 33.33% or my 31%?

It's interesting, for sure.

But I'm curious where you got the 77% reduction figure from (80 M/S vs 343 M/S in air): that sounds way too high, and I didn't see it referenced in the thread.

For now, I'm sticking with my 31% figure, but I'd love to see the real figure nailed down, either by math or empirically.

- Stuart -

[DanDan]

Hi Stuart, thanks for the comments. This popped up in another thread, which I will find in a little while. The Topic was VPR but a few guys did the math. From memory 88 m/s 50Hz 10K Fibre. Another was 111 m/s 100Hz.
IMO these figures to be not really credible. Surely they would make a nonsense of Mode Calculators and such? Surely someone would have noticed. But then the HH formula was wrong on studiotips for years...... And the Math boys checked their work, and are sticking to it. My fibre is light attic insulation, mad guess 5K GFR. Perhaps this accounts for my relatively small 37% change in frequency. Or huge!
https://www.gearslutz.com/board/showpos ... ostcount=6

Just to keep things together here rather than jumping fora here's the little test:-
The mic didn't move. I don't have any other insulation handy like that one. I did try with just one roll which kinda half filled the tub, but it came up with some nonsensical much higher Fc, light that of a half tub!

The Images should say it all here. But for those who want to do the Math.
Speaker height, middle of woofer to floor of tub = 85cm
Tub= 66cm
EcoWool stack of two rolls 80cm
Eco Wool came from B&Q UK Chain store. GFR or Density unknown, made from recycled plastic bottles. I presume Polyester?

Fc Empty Tub = 98Hz
Fc Stack in Tub = 61.9Hz

I had been racking my braincell to come up with a test to find out if sound travels slower in fibre as theory suggests. Thank you JohnPM for the suggestion.
While the rig is in place, any requests?

EMPTY TUB


ECOWOOL IN TUB

[Soundman2020]

From memory 88 m/s 50Hz 10K Fibre. Another was 111 m/s 100Hz. IMO these figures to be not really credible.

Very much agree! I've never seen such a huge change in modal frequencies as to suggest that much slowing down! You always get changes in frequency, for sure, but nowhere near that large.

Surely they would make a nonsense of Mode Calculators and such?

I'd agree with that too. Yet, the calculators seem to do a pretty good job! Adding deep absorption to a room does make the room appear "longer" (lower frequencies for the modes in that direction) than the calculators predict for empty rooms, but certainly not off by anything near 80% of the absorption depth!

I'll go through some of my REW data for rooms I've treated, and see if I can find anything useful, but I'm pretty sure I would have noticed if I put a foot of mineral wool on the rear wall, and it acted like four feet of insulation! Mostly I see changes of a few percent in modal frequencies, which ties in well with the "roughly 20% to 30%" reduction in the insulation.

By that I mean that a change of a few percent TOTAL implies a change of about 30% in the wool, considering the entire room length. Thus, a room 133 inches long (11'1") would have an axial mode at 50 Hz. If we put a 13.3" absorber on the rear wall (10%, for simplicity) means that the wave moves at normal 343 m/s speed through roughly 10 feet of air, and is only slowed down by 30% in the remaining 1 foot (roughly). Thus, the change in speed or frequency for the full room is going to be about 3%. That's what I usually see: changes of maybe 1, 2, 3, 4, 5% in typical rooms of typical lengths with typical treatment. On the other hand, if this strange theory is true, and the speed slowed down by 80% in those 13.3" of insulation, the TOTAL frequency should shift by about 8% (since the insulation is only 10% of room length). Thus,that 50 Hz mode in that hypothetical room should now show up at 46 Hz, and if you double the thickness to 26.6" of insulation in there, it should show up at 42 Hz. With 39.9", it should be down at 38 Hz. etc. I don't recall seeing such large jumps in rooms I have done.

Like you, I'm finding it hard to buy that 88m/s vs 343m/s change at 50Hz, which is a pretty common modal issue in may small rooms. I'm certain such a large change would have been seen and documented by now, if it actually occurs in the real world.

Surely someone would have noticed.

Bingo!

My fibre is light attic insulation, mad guess 5K GFR. Perhaps this accounts for my relatively small 37% change in frequency. Or huge!

Could be. Also, you are measuring at around 100 Hz, not the 50Hz those guys are talking about, so maybe that's why you got such a "small" number? Is there any way you could get a lager tub and try for 50 Hz? If they are right, the frequency should drop to 12.5 Hz, which I find pretty hard to believe.... Not even sure you'd be able to measure accurately that low with REW... MY guess is that if you could get 50 HZ, adding the insulation would be similar to what you got here: it would go down to maybe 35 Hz or so.

Thanks for the link! But as they say, the THEORY is fine, but what about in PRACTICE?


- Stuart -

[Soundman2020]

OK, you got my curiosity up! So I went looking at real data from real rooms, to see if I could measure a real effect in real life, and I didn't have to go very far: A room I'm working on right now for a customer in New Orleans. Long story, but he basically did all of the front of the room first (soffits, hangers, bass traps, cloud, etc.), then built the rear isolation wall towards the end of the process, and treated that. So the room isn't too bad at all after the iso wall goes up, since there's already a good amount of treatment up the other end, but there are still some clear modal things going on, albeit low level.

So here's the situation right after he built his isolation wall, but before the rear-wall treatment went in:

STVNO-ISO-39.4.png

As you can see, there's a small modal thing going on at at 39.4 Hz (as near as I can nail it).

Then we put in the rear treatment: a total of 21" deep, including FRK on the isolation wall (which was built inside-out), hangers, then 703 on the front face, and fabric. Here's what that accomplished:

STVNO-REAR-BASS-38.6.png

You can clearly see that the modal thingy dropped to about 38.6 Hz (the cursor shows 38.7, but I zoomed in a bit and got 38.6).

So do the math: 38.6 / 39.4 is a change of about 2%. The room is nearly 29' long, and that's the 2,0,0 axial mode. So, there's 21" treatment over 348" room length, which is 6%: thus, the sound is traveling at normal speed for 94% of the room length, and slows down for 6% of room length. In that 6% the frequency changes by 2% overall. That's a change of about 33% in the insulation alone... Roughly what I would have predicted. Roughly what Andre says. Roughly what you found in your experiment. And a far distance from what this theory predicts.

If the strange theory were true, it should have changed by more than twice as much: the mode should have dropped to about 36 Hz. Nope. Didn't happen.

There's a few other modal peaks down in the same region, and they also changed by about 2%...

Color me skeptical...


- Stuart -

[DanDan]

Isn't this bizarre? Another one claiming 100m/S. Page 9 http://www.torean.dk/artikel/Absorber.pdf

[Soundman2020]

I'm not so sure I'd take that paper as Gospel: There's a lot of strange claims he makes in there without any reference, discussion, or proof, and some of them are rather bizarre. For example, on page 4: "The absorption coefficient is maximum when there is no reflection from the surface so all energy enters the sample and is dissipated, and minimum when there is full reflection, which means that no energy enters the sample. " Wouldn't it be nice if that were true in the real world! Or his claim that the classic "open window" is a good example of a membrane trap! and in the very next paragraph claiming that a perforated panel trap works in the same way as a membrane trap ... Last time I checked, perf panel is Helmholtz, not membrane. The panel itself might possibly have some minor membrane characteristics, but the actual mechanism for absorption in a perf panel device is 100% Helmholtz. If it was not, then slot walls would not work! Slot walls are a special case of perf panel. There is no membrane action at all in slot walls. Yet: "A perforated rigid plate is more robust than a thin membrane and performs in much the same way". Hmmm.... Even stranger, he then goes on to use perf panel as the typical and ideal representation of a Helmholtz resonator! So even though he already said that perf panel is a membrane trap, he also then says that no, in reality it is pure Helmholtz.... Go figure.

In that section, he makes this rather strange claim: "the resonance frequency should equal 290 Hz using 10 mm plate thickness, 1 mm radius of the hole, 10 mm spacing centre to centre between the holes and 100 mm from the rear of the perforated plate to the rigid surface." He's off by a factor of about of about 200%! Plug in those exact numbers to the "acoustic modelling" website model, and you get a frequency of 148 Hz, not 290 Hz. Right next to that he shows another graph for the exact same situation, except that he filled 50% of the volume with porous absorption. And now the resonant frequency inexplicably INCREASED (yes, increased....) to 350 Hz... Ummm.... I'd love to see his explanation for how he managed to get the resonant frequency of a system to increase simply from adding absorption... especially when he claims that porous absorption REDUCES the speed of sound by huge factors.

He also appears to confuse surface density with specific weight in some places... And he invents or misuses terms in other places. For example, check out his continued use of the term "specific mass" throughout the paper... Now try to google a definition for "specific mass" and see what you come up with...

Another strange claim: "The propagation direction within many porous absorbers is approximately normal to the surface, even for oblique incidence sound." Hmmmm..... So all randomly incident sound instantly normalizes itself as it passes through the surface... an interesting hypothesis!

No- Just no. His math is flawed, his explanations are flawed, his understanding is flawed, his predictions are flawed.

In addition, the claim for 100 m/s applies to prediction for impedance tube measurements: The real world is not an impedance tube! That might be true (still skeptical with no proof of the claim) for plain waves and normal incidence, but certainly not for random incidence and non-planar waves. He even states a figure of 180 m/s with a cryptic claim saying he acquired that from a non-functioning page on Rockwool's website.

The forward of that paper states that it is just a "self-study" effort, and therefore is ungraded and uncorrected, as well not being peer-reviewed nor published by a recognized university or faculty. So it's not even an undergraduate paper, and certainly not a graduate thesis. It seems like that paper was just his attempt to try to understand some of the theory, and he create a series of flawed Matlab models based on that flawed understanding. He then presents the graphs produced by that data as though they were Gospel truth, even though they are way off from actual reality.... He does no testing to verify his predictions: just assumes that the predictions must be written in stone, because he wrote an equation for Matlab, and Matlab solved it....

I'm not buying it.

I would not give any of his claims or comments much weight. Or mass. Or density. Or specific density. Or specific mass (whatever that is!)

Color me skeptical still.


- Stuart -

[DanDan]

Hmmmm, thank you. Colour you clear to the point of transparent! I didn't read the paper, so my apologies for sort of wasting your time and effort. I only noticed the 100m/S bit. The Math seems to be the same which fooled Mike, mpos, (NorthWard employee) and Demetris, prairiedog. (acousticmodelling.com) I have been assured by quite a few that the 'Math' is correct. None other than Mike go so far (out) as to state that such speeds actually occur though.
Mental reservation.
What fascinates me here, is that in reality we all know it is about 19-37%, but quite a few are insisting on this Math/Myth quarter speed stuff.
Thank you for the clarity Stuart.

[AVare]

Nice research Stuart!

Andre

[Soundman2020]

Nice research Stuart!

Andre

Oh COOL! Andre is back!

Man, you have been very sorely missed around here, Andre! Your one-line to-the-point pithy replies are ALWAYS spot on ... and badly missed

I really, REALLY hope you stay!

Hopefully,

Stuart.



(PS. Thanks for the kind words! Coming from you, that means a lot. You are the one that got me hooked on acoustics, all those years ago...)

[camsr]

Do the SPL readings reflect correctly the level drop associated with adding the absorber into the cavity?
What would account for the lower resonant frequency, surely not volume since that has been reduced by the addition of insulation.

[Soundman2020]

Do the SPL ....

.
Please read the forum rules for posting (click here). You are still missing something!

To answer the actual questions, since they might be useful for others:

Do the SPL readings reflect correctly the level drop associated with adding the absorber into the cavity?

I'm not sure which "drop in SPL readings" you are referring to, but in general the SPL level will drop at the frequencies where the mode or other resonance was before the insulation was introduced, because the resonance has now been damped. It might not drop completely to the reference level for other reasons, but there's usually a reduction.

What would account for the lower resonant frequency, surely not volume since that has been reduced by the addition of insulation.

The volume has NOT been reduced: the volume is the exact same as it was before. What has changed is that damping material has been introduced into the volume. That damping material produces several effects, once of which is to lower the speed of sound inside the volume where the insulation is. Since sound travels SLOWER in that part, it makes the room appear LONGER than it really is. Also, slower speed = longer wavelength = lower frequency. In other words, if it goes slower, then it appears to travel a longer distance, thus the frequency goes down. Having insulation in that volume also does other things, such as changing the way the air deals with heat, from adiabatic to isothermal. The insulation also has other effects on the sound that tend to reduce the frequency.


- Stuart -

[DanDan]

Bienvenido Andre. You will remember that I approached various people who I considered have superior Math to myself. I got to Engineering level, but that was many decades ago and it is not really used much in day to day Acoustics and Noise Control. My question was the same as here in this thread. i.e. "This Math presented by mpos states that sound travels at speeds as low as say 88m/S in fibre.
I am gobsmacked, kinda doubt it, so as a favour to me, could you please check the Math. "
prairiedog the author of the Online PAC seems to have gone with the Math, although he was kinda gobsmacked too.
John Brandt had a go at the Math, but another trusted number cruncher contradicted him.
Thomas Jouanjean backed up his protege mpos, saying "The Math is correct" but didn't go so far as to say that sound actually does slow down to a quarter or so.
I am quite assured that my/our natural instinctual understanding, backed by observation of an utter lack of this quarter speed in practice, is correct.
My question now morphs to how can such a basic physical behaviour and the in Engineering terms, relatively simple Math describing it, be so differently interpreted?
Could you pass the Aspirin please Andre?