The room treatment thread

[w00key]

There, put my thoughts in one place @ https://imgur.com/a/wz9fS8U

It turned into a pretty big slide deck but now I finally have a feeling for designing these magic boxes.


Common fails:

- people read about resonance frequency, but forget the optimal size rule, or absorption cross section formula. Then you get tiny resonators, lots of it, that do nothing.
- related: if you divide aperture (opening) into several smaller ones, the resonance volume goes down with it. Don't do that.
- forgetting about Q. Too high means it is unusable in real life, but lowering it by stuffing needs to be done really carefully, single digit Rayls is enough.
- ignoring resistance. At tiny hole sizes, the boundary layer of air above the solid works as resistor, but if you want to kill bass, and you remember the single hole > many tiny one rule, you NEED a porous absorber layer or you get infinity Q.


It also contains a magic box design that works as broadband bass trap, equal to an open window:

Spoiler

(it is 105x105 cm though, so absorption coefficient peaks at "only" ~1.3.)


Time to turn one of them into a test design. Maybe I'll do a small scale 82 hz test model first, that one may be placed anywhere along the long wall. Or a 80-90hz corner model above the subwoofer, 50x50x50 triangle works in Excel.

 

[Blaspheme]

The slide deck is excellent.

I'd guess the thin array and/or perforated variations came about initially with space constraints, and things like drop-in ceiling grid panels are decent to address eg workspace noise. Since that isn't this, I'm now thinking more about using larger volumes in room dead space, and perhaps furniture-like constructions.

I'm also wondering if placing the port/hole near the edge for eg corner placement (or maybe bottom/top for vertical/axial or tangential mode treatment) is advantageous (or not). You mentioned corrections for offset holes a while back: does hole position make much difference (moving to eg room corner may help, moving toward edge of chamber face may change variables)?

 

[continuum]

I am very curious how this works out for you.

The dimensions, if you have a free corner to put them in, might not be too unreasonable.

And the more I read through your calculations, the more I realize how lucky I am (and did not appreciate it til now) that I was able to stick one of GIK Acoustics' tri-traps from floor to ceiling in a corner... that's actually a lot more volume than I thought about.

 

[w00key]

Re: normal traps: ah yeah, that would be much easier, but this kinda turned into a hobby now. It's amazing what you can dig up on Google Scholar, but unfortunately, no new insights. Everyone (even researchers) don't mention or measure σa1

Absorption is easier to get funding for I guess? Just need a tube and 2 mics, especially for smaller devices.

~~

I reread a section about the infinite wall formulas and noticed something.

The analysis of a single resonator in a wall is very closely related to that of a resonator in a free field. The only difference is that independent of the frequency the "blocked impedance" pressure at the aperture is now equal to 2P0, i.e., twice the incident pressure, and the radiation resistance of the aperture is twice that of the resonator in a free field.

Formula 47:

Formula 47 is inconsistent with the next paragraph though in the example, so not sure what Q1 on a wall should be:

Is Q1 x1/2 or x1/sqrt(2)? Grmbl how did this get through peer review?
I guess I need to dig into the wall of formulas (brr) and follow the steps of deriving it.


But the moment was:

Wait, if pressure increase does this, what about a wall to wall corner area? That should double the effect. And on the floor or ceiling tri-corner, it's even more. Hypothesis:

That would make the radius 0.77 times the on wall radius, and 0.47 times the volume due to the a^3. Q is lower, which is always good, but absorption cross section, did that just get a 4x boost from the wall calculation? That would be epic. (50hz = (343/50)^2*2/pi = 30m2. That would be far too much.)


And something's probably wrong in the existing xls, I'm getting silly large apertures like 500mm, just leave the front off, so probably time to start a new sheet (web based?) and add support for corner/tri-corners to it.

 

[w00key]

I did not know Google had hosted Jupyter notebooks nowadays, this is pretty cool.

https://colab.research.google.com/gist/ ... oltz.ipynb


This is much more readable than F "=1+(9/16)*(C35*C24)^2*(1+COS(ASIN(C21/C24)))^2". Excel sheets are completely undebugable. Last term should be arcsin(r0/a), but written as arcsin(A/a), but effect is pretty minor, F is basically static.

Fixed version: =1+(9/16)*(C35*C24)^2*(1+COS(ASIN(C18/1000/C24)))^2


Absorption cross section seems wrong too on the on wall tab, sqrt(4*(4* instead of 4*, weird. And this time effect is not that minor... That's what you get for building a super complex model in Excel

Throwing in a perfectly sized cube doesn't give me sabins = max possible sabins at frequency, so yeah, something's really borked. Oh well. Time to rebuild it in Python, but I'll probably take it easy and do it in little steps, not in a hurry anyway.


It's like I'm back at school, crazy how no one ever (that I could find) built a decent tutorial for this.

 

[Blaspheme]

That notebook is much more readable, I was having trouble parsing a few of the formulae previously.

I did notice that plugging in some of the optimal sizes didn't always display better sabins in shaun's workbook. Good to know that's not just my error/ignorance. At this stage I can select sizes from w00key's work, than get a port size from shaun's (the very big ports are also suspect, I think, but otherwise it's helpful) to scope things.

I'm going to map my room modes grid-wise when less busy. There's potential for a large absorber volume in a back/side corner recess in the current layout.

 

[w00key]

Well I picked up this research again after discovering some severe gaps in frequency response. Moving a block of rockwool (600 x 500 x 280mm) to the top-back-left corner fixed it up enough that the DSP can magic away the rest. acousticmodelling.com/porous.php says this:

After Audyssey did its magic, there are still room modes that are unkillable - measured at center seat:

It did a good job with 25 (1st long edge), 37 (1st short edge), 46 (1st corners), 51 (2nd long edge), but 70 and 140 are holy crap bad.


Oh, that's the ceiling (concrete) - floor (wood) mode. What the hell am I supposed to do about it without carpeting the room? No wait, that doesn't work anyway, at a boundary - walls, ceiling, floors, the velocity is zero and any porous absorber don't work really. (recap on velocity vs pressure).


Helmholtz. Time to dig into more greek. I have sort of decoded the Helmholtz3.xls now and put a bunch of new calculations on Helmholtz.ipynb.

But the most overpowered part of it is Ingard1953, page 15, formula (47).

On an infinite wall with 1 resonator, pressure doubles and the absorption cross section doubles too. Q1w is also lower, by Q1f*1/sqrt(2) (yes that's an error in 47 or it would be REALLY OP), and optimal sphere radius goes down too by 1/2^1/6 (4/3*r^3*pi = resonator volume in m3).

But what if you put it on a wall-wall edge, like the front wall x ceiling edge? Pressure doubles again as it has half as much ways to escape. Corner? 2^3 total effect?

(20):

In xlsx this turned into an abomination like =((C39)^2/(4*PI()))*((4*(4*4*4*C38)*(C35*C24)^6)/(1+(2*2*2*C38)*(C35*C24)^6)^2)*C37 where C38 is C - it seems to match up with calculating using old-skool design charts.


My new theory on the weird 4x4x4 is that the first term, λ0^2/4π, should be /2π for a wall, /π for edge, /0.5π for a corner; this follows from (47) part 1, where σα1 which was λ0/4π gets a x2 -> λ0/2π. And C / C38 should be doubled then in both numerator and denominator. Without this the numbers don't match up with examples given in the paper. So cleaned up formula, where 1/2^x or 2^x -> x is 1 for wall, 2 for edge, 3 for corner, becomes

=((C39)^2/((1/2)^3*4*PI()))*((4*(2^3*C38)*(C35*C24)^6)/(1+(2^3*C38)*(C35*C24)^6)^2)*C37


If I didn't bork anything it seems to say a 60x54x30 box, partitioned in 1/3 and 2/3, with different tuning frequencies, can act as a 40-140hz broadband absorber with an absorption cross section that peaks at 5 m2. For a frontal area of .324 m2.

Of course > 100% efficiency isn't that exceptional with good placement, GIK sells edge traps that are 120x40x40 and have 18 sabins (=1.8m2 x 100% absorption cross section or 375% of a perfect absorber but placed in a x1 spot), but 1540% is a bit... extreme. It is equal to a hole in the wall of 2.5 x 2 meters, that's insane.



Sleeping a year on the paper seems to help, last time I had way more trouble with all the greek letters heh. What a dense pieces of research, 25 pages of condensed information...


After poking at it for a while you get to designs that no one else makes - one BIG hole instead of multiple (figure 7 says don't) and the importance of damping (page 16/17, A Note on the Damping of Resonators), but don't overdo it, filling it with 10000 Pa*s/m2 rockwool totally kills it, additional resistance is at least one or two zeros too high -> extreme low Q (specificity) and extreme low σα due to optimal sphere radius / volume going crazy high.

My Q=1.5 design which are crazy wide band for a resonator have 5.02 and 1.73 Rayls of additional resistance, how to get to that is going to be interesting, Rockwool is 10000 Rayls, probably start with none, then something like a single paper in the port? We'll see...

 

[penumbra]

I find this thread fascinating but I think you are not adequately paying attention to the loudspeakers you are using. I design large sound systems for a living: theaters, churches, train stations etc. One of the things we typically do is try and get as much of the acoustic energy as possible to where people are and as little as possible on the walls and ceiling. I use software called EASE to model rooms with loudspeakers but typically only large sound system speakers are measured so that their data is available. I don't think I've ever seen real (i.e. believable) polar plots of consumer loudspeakers so you will have to determine for yourself.

Take one of your speakers and elevate it enough so that you can walk around it and listen to it from various angles. Outside is best so the room doesn't affect things. Play pink noise through it at a reasonable level (pink noise is easily available on the web). Walk around the speaker and move your head up and down. Most non-coaxial speakers have a weird anomaly that is in line with a point between the woofer and tweeter; there are often many other interesting peaks you can find. I typically just use my ears but a meter could be helpful if you are unaccustomed to evaluating speakers this way. Some speakers beam the high frequencies to a rather tight point, others have significant lobes from crossovers and/or driver interaction. Pink noise is great for this because there is a noticeable shift in timbre with increase and decrease in high frequency content.

I use recording studio monitors at home because one of my primary listening goals is clarity of sound. The Mackie HR824 speakers I'm using now in my living room have a much wider dispersion pattern than I would like so will replace them eventually. They however don't have other issues significant enough to really bother me. I have someone living beneath me so for their sake, I don't want speakers that I'm inclined to turn up even louder.

Edit: By knowing what frequencies and direction your loudspeaker is putting out sounds you can better place your absorption.

 

[thrillhouse]

I have nothing whatsoever to add, but I'm following this thread with great interest. Amazing stuff.