I read this part the first time thru, but I guess it didn't stick while I was looking for the dimensions of the opening. Am I missing the calculations for w, too?
"The width and thickness of the unit are D=λ0/2 and λ0/20, respectively. In this study, the neck width of the cavity w is the only tunable parameter for controlling the phase shift of the metastructure unit."
"The width and thickness of the unit are D=λ0/2 and λ0/20, respectively. In this study, the neck width of the cavity w is the only tunable parameter for controlling the phase shift of the metastructure unit."
Yep, either way you have λ0/2 as a dimension. Unless Bill's suspicion of a chosen ration is correct.
(thanks for the subscript!)
Worse for lower frequencies IMHO, because you have use the better portion of a wall to treat a single octave or so. Smaller panels can be stacked, hung, etc in front of the lower panel, a la Simon, which could look very interesting as long as they don't interfere with efficiency of the larger panel.
I wonder about damping the front panel on a low frequency model. At 343 Hz, λ/2 is 50cm, that's a half-meter square panel over an empty chamber. I could find no mention of front panel thickness anywhere, I'm sure a thicker panel would affect the f0.
AFAIK, they're snuggled up with Bill's eigenvalues, a Do Not Disturb sign on the door.
If each cell is 20"x20" in wall area to get down to 350Hz, then that's also the spacing between the centers of their ports. Seems like the sound source and the listening position both would then have to be way far from the diffusor so things can approximate equal distance, plane wave-ish, from each cell? For a step diffusor, the cell size (or strip width) limits the high frequency effectiveness also, if the same is true for the metasurface diffusors then that would seem likely to be a limitation in reaching higher frequencies.
Putting one in front of the other (if that would even work -- isn't it meant that the broad areas don't pass sound pressure through??) would make for a thick overall assembly. Might as well just do a step diffusor if so.
Putting one in front of the other (if that would even work -- isn't it meant that the broad areas don't pass sound pressure through??) would make for a thick overall assembly. Might as well just do a step diffusor if so.
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Personally, I wouldn't plan on doing any layering that would cover the openings of the panel in back. For that matter, the solid portions of the front panel are assumed to be reflective in this study, aren't they? I guess a small HF panel between the openings of a large LP panel wouldn't be disruptive given the distance between frequency ranges.
I agree that the step diffuser looks like a better alternative for some, if not many, cases. Regarding LF panel size, it looks prohibitive for anything but a large room to me as well. But I'm no expert here.
Regarding your eigenvalues, are p,q,r corresponding to "room" modes created by the internal cell dimensions?
I agree that the step diffuser looks like a better alternative for some, if not many, cases. Regarding LF panel size, it looks prohibitive for anything but a large room to me as well. But I'm no expert here.
Regarding your eigenvalues, are p,q,r corresponding to "room" modes created by the internal cell dimensions?
I believe so, but I just don't have any idea what to put in for them in the formula. Maybe just up to some integer (2?) for each?
Though, looking at the dimensions and the sizes of the cells needed to get into the lower midrange, I'm not too encouraged to make these now. Resonators are by nature narrow-band delay generating devices, while steps or wells are broadband delays. Unless the depth advantage is more than a few inches -- to make the tradeoff in bandwidth and area versus device depth worthwhile -- it doesn't really seem worth it. I'm wondering where such diffusors even make sense -- it seems that they need a big room to fit in all the cells and to have listeners and sources far enough away. But in a big room, who really cares about a few inches of wall depth?
I've been playing with ambience (delayed omni, added) speaker drivers, which seem to be an even smaller and easier way to get some of the same effects. Not for breaking up early reflections, of course, but for increasing ambience and perceived detail and apparent room size. Such schemes do use digital delays and non-coherent speaker drivers, though, which we all know are heresy, travesty, and the devil's own work to any self-respecting audiophile!
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The author I contacted said he will pass along my email address to the principal author, who can answer more questions. I'll be sure to ask about the wall dimensions and the opening size. If this new diffuser simply trades depth for width, it's a lot less useful than I thought. Still worth finding out, though.
As I understand it...
Yes, they are integers that correspond to the harmonics. Use 1 for the 1st mode, 2 for 2nd harmonic, etc. Use p, q, r corresponding to l, w, h.
A 1 for p, and 0's for q & r will give you the first axial mode for the dimension indicating length. A 2 in this position instead will give you the 2nd axial harmonic for the length.
A 1 for p & q and 0 for r will give you the first tangential mode for the two horizontal dimensions.
0's for p & q and a 1 for r will give you the first mode for the vertical dimension.
Don't take all that to the bank without someone else's nod of approval, it could be tainted by the gray hair from whence it came.
Yes, they are integers that correspond to the harmonics. Use 1 for the 1st mode, 2 for 2nd harmonic, etc. Use p, q, r corresponding to l, w, h.
A 1 for p, and 0's for q & r will give you the first axial mode for the dimension indicating length. A 2 in this position instead will give you the 2nd axial harmonic for the length.
A 1 for p & q and 0 for r will give you the first tangential mode for the two horizontal dimensions.
0's for p & q and a 1 for r will give you the first mode for the vertical dimension.
Don't take all that to the bank without someone else's nod of approval, it could be tainted by the gray hair from whence it came.
In my adaptation, for the low frequencies I can make a cell 5' x 5' that would require a depth of 6" the opening would be 6" x 6". In front of this would be a panel 1.75" deep that is comprised of nine varying cells each with 3" x 3" ish openings. They would not cover the opening of the low frequency cell. Finally for the top layer there would be averaging 6" x 6" cells .75" deep with widely varying openings, again none blocking the other ten vents.
What I think is still open is if the opening should be centered on the resonant cell.
This would produce a wall unit .75" + 6" + .5" + 1.75" + .5" + .75" + .5" deep. A thicker back is needed because it is unbraced. The rest of the front/rear walls are braced, thus thinner. So the finished unit would be less than 11" deep, it will however be a bit heavy.
If there are additional small braces in the large chamber they may be used to set up other resonant modes.
A classic Schroeder panel of 11" maximum depth would work down to about 200 Hertz. This design should work about one octave lower.
I don't consider this to be an advanced woodworking project.
What I think is still open is if the opening should be centered on the resonant cell.
This would produce a wall unit .75" + 6" + .5" + 1.75" + .5" + .75" + .5" deep. A thicker back is needed because it is unbraced. The rest of the front/rear walls are braced, thus thinner. So the finished unit would be less than 11" deep, it will however be a bit heavy.
If there are additional small braces in the large chamber they may be used to set up other resonant modes.
A classic Schroeder panel of 11" maximum depth would work down to about 200 Hertz. This design should work about one octave lower.
I don't consider this to be an advanced woodworking project.
That's pretty much exactly what it reads like. And the magic is in the hole size. Haven't have a good chance to read carefully enough to really think too much more deeply on the design. And while I had to do *some* calculus by hand last week, I'm a bit away from feeling comfortable with those equations! (A younger me is judging harshly I'm sure)
But the formula presented in the paper is generally:
1.) Pick a central frequency; at best you'll bet about an octave below and 2 above.
2.) Your cavity width is lambda/2 and your cavity depth is lambda/20.
3.) Good luck on the hole size.
Could be useful if economically designed to cover LARGE areas unobtrusively, but doesn't seem to have nearly the same oomph/sqft as a QRD.
I suspect the way to go would be to use the chosen lambda value and run an array of values of w (or Sd) through the formulae and draw a spline curvefit of that parameter vs. tuned frequency. After deciding what p and q values to play with (r=0 is the only case of interest).
Of course that's assuming there are answers for my questions about S, Sd, w, w^s...
Of course that's assuming there are answers for my questions about S, Sd, w, w^s...
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Agreed. But since the cell size is constant, it should be possible to generate a curve of resonant frequency vs hole size. Though we really need frequency and phase vs. hole size (unless the phase shift at a %offset from resonance at a given frequency is pretty predictable with another curve?). Eventually, need to be able to start with a frequency and a phase shift and get a value for Sd or w. Then: start with frequency, figure the frequency shift from resonance needed for the phase, use that to calculate resonant frequency (where phase goes through 0).... look it up on the curve-fit to find Sd or w. Sounds like a blast.....
Another question is whether the hole can be round.
Another question is whether the hole can be round.
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Wonder if there's something like this that's the right size. Would sure simplify construction.
Textura de madeira grade de Metal de aluminio forro cor Custom made 2 metros de comprimento por partes Loja Online | aliexpress movel
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Sd was indeed specified as w2. (thanks again Pano!)
The w2 in your quote looks more like ω2, as in angular frequency squared.
I would interpret Sd*ω2 as (surface area of the hole)*angular frequency2, I dunno about just plain S. Hmmm...
It could also be shipped in flat packs if needed.
It could also be shipped in flat packs if needed.
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