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QRD diffusor well width question Diffusion Products
Old 1st February 2011
  #1
Gear maniac
 

QRD diffusor well width question

Hi All,

I have Everest's Master Handbook of Acoustics and specifics on QRD diffusor construction are sketchy at best. Couple questions related to well widths/spacing.

I understand that well width is related to the effectiveness vs frequency of a given unit, but do I need to maintain any certain proportion between well width and depth or are the two independent of each other?

Also, if well width is a parameter I need to take care with, do I need to factor in the width of the well dividers as well?

Thanks!
Old 1st February 2011
  #2
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I'm in the midst of designing some 1D qrd's right now (are you doing 1d or 2d?). I'd highly recommend downloading a free program called QRDude - it's a calculator / designer for QRD diffusers. I can't imagine the mind-boggle of working without it lol! I'm using 1-inch well width (not including the well dividers - I'm using 1/8" for those).

http://www.subwoofer-builder.com/qrdude.htm
Old 1st February 2011
  #3
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jhbrandt's Avatar
QRDude is 'ok' and replicates many commercially available quadratic residue diffuser designs. The 1Ds are normally built using the sequence twice in a mirror-image side-by-side configuration. The 2Ds are designed using the sequence 4 times, which, IMO is not ideal and will produce more lobbing.

If you plan on building a 2D diffusor for a wall or ceiling, the ideal route would be a single sequence PRD with zero repeats. You can design these with the help of the calculator online here.

For a better understanding of how the math works for 1D diffusors you can download my Excel calculator, 'Build your own Quadratic Residue Diffusor', available on my publications page.

Cheers,
John
Old 1st February 2011
  #4
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Glenn Kuras's Avatar
Quote:
For a better understanding of how the math works for 1D diffusors you can download my Excel calculator, 'Build your own Quadratic Residue Diffusor', available on my publications page.
Wow John that is some great information there. thumbsup
Old 1st February 2011
  #5
Gear maniac
 

Thanks for the link. I'll check that out when I'm starting the design process. It first seem to have any information that addresses my original questions about width though. I'm on an iPod so perhaps it didn't display quite right or I missed something?
Old 1st February 2011
  #6
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Nordenstam's Avatar
 

Mayhap this helps? Effective frequencies of a diffuser
Old 1st February 2011
  #7
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All useful information, but still doesn't directly address my question:Do I need to maintain a specific well width to well depth proportion or are they totally independent of each other?

I might assume that they are independent of each other since I have run across no references saying otherwise, but neither have I come across any information corroborating this assumption.
Old 2nd February 2011
  #8
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jhbrandt's Avatar
Bob,

Sorry, if I was too vague in my earlier reply.

Simply put; Yes, there is a relationship which sets the bandwidth of the diffusor. Too large a bandwidth can reduce the efficiency of the diffusor. For this reason Diffractals were designed. My recommendation would be to set the bandwidth to cover only about 2 octaves maximum, ie; from 500Hz to 2kHz or from 1kHz to 3kHz.

The well width determines the HF cut-off & the diffusor depth determines the LF cut-off. Also note that diffusors are often effective to 1.5 times the cut-off frequency.

When designing a custom diffusor for a particular room it is important to determine the regions of sound for that room. For example; a room that has the dimensions H = 350cm (320.9"), W = 560cm (220.5"), and D = 815cm (137.8") that is treated so that the averaged decay is about 0.4 sec. (RT-60) will have the following regions:
F1. (low frequency cut-off) = 21.09Hz
F2. (beginning of transition/diffusive region) = 94.73Hz
F3. (beginning of Ray region) = 378.91Hz
F4. (high frequency cut-off) = 20kHz ** sound does not cut off, but our attention does.

The diffusor recommendation for this room would be for a diffusor that has a design goal bandwidth from 756Hz to 3kHz. This diffusor would effectively cover the spectrum from 378.9Hz through to 9kHz - & that's plenty!

For a better understanding of the relationship of well width and diffusor depth get a copy of "Acoustic Absorbers and Diffusers" by Trevor J. Cox and Peter D’Antonio. Good luck!

Cheers,
John
Old 2nd February 2011
  #9
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I'd previously checked out that book online, but for how far my interests extend in to the realm of acoustics it doesn't feel like a reasonable expense.

Thanks for the response though, directly answers my question here.
Old 2nd February 2011
  #10
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John is correct (of course) but it is slightly more complicated than that. The effective bandwidth also depends on the overall panel dimension of the diffuser.

This is discussed at the QRDude web site where Collo has done (IMO) an excellent job of distilling a lot of the more technical and complicated info from the Cox/D'Antonio book.

Quote:
The 1Ds are normally built using the sequence twice in a mirror-image side-by-side configuration.
John, are you saying that a QRD is symmetrical? It is "almost", but cannot be as it always has an odd number of elements. QRDude allows for "shifting" the sequence to make it even less symmetrical if that's what you prefer.
Old 3rd February 2011
  #11
Gear maniac
 

Thanks, I think I'm gonna try to find a computer to run QRDude on. Looks like a very useful app.

I just realized today that part of the thread title, QRD Diffusor, is redundant. Sort of like saying ATM machine.
Old 3rd February 2011
  #12
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jhbrandt's Avatar
Quote:
Originally Posted by Sebg View Post
John, are you saying that a QRD is symmetrical? It is "almost", but cannot be as it always has an odd number of elements. QRDude allows for "shifting" the sequence to make it even less symmetrical if that's what you prefer.
Well, most 1D devices have the sequence repeated in reverse order, even the RPG units & yes, they are symmetrical. It is not recommended to place identical units side-by-side. The QRDude calculator is great. - but it does place a 2D design 4 times on the grid. I would only ever use one of those on a single surface.

The PRD calc on prime's site is excellent and does not repeat the sequence or well dimensions. (set the resolution to .1cm before you calculate).

Here's a brief list of possible input data:

PRIME ..... LPR ..... ARRAY
13 ..... 2 ..... 3 X 4
43 ..... 3 ..... 6 X 7
89 ..... 3 ..... 8 X 11
157 ..... 5 ..... 13 X 12
241 ..... 7 ..... 16 x 15
307 ..... 5 ..... 18 x 17
523 ..... 2 ..... 29 x 18
547 ..... 2 ..... 26 x 21
571 ..... 3 ..... 30 x 19
661 ..... 2 ..... 33 x 20
1093 ..... 5 ..... 39 x 28
1103 ..... 5 ..... 38 x 29
1117 ..... 2 ..... 36 x 31
1151 ..... 17 ..... 46 x 25
1613 ..... 3 ..... 52 x 31
1871 ..... 14 ..... 55 x 34
2221 ..... 2 ..... 60 x 37
2243 ..... 2 ..... 59 x 38

Cheers,
John
Old 3rd February 2011
  #13
Gear Addict
 

Sorry, John, I still don't follow.
Quote:
Well, most 1D devices have the sequence repeated in reverse order, even the RPG units & yes, they are symmetrical
Are you talking about single diffuser panels or multiple panels side-by-side? Multiple panels should be done according to some modulation sequence, such as Barker. Discussed by Cox and D'Antonio and also explained on the QRDUDE site. The "off" panel has to be significantly different from the "on" panel - instead, very often people just use the same panel rotated 180degrees. is this what you are saying?

People always have other options - especially with DIY. eg an N5 instead of N7 panel, a shifted panel, an inverse panel. Since most panels in a modulated sequence are still "on" panels then having a different design freq for the few "off" panels is not a big deal. This is all discussed in the literature and on the QRDude site.

Regards the 2D panels that QRDude produces, it uses the exact modulation sequence from the Cox and D'Antonio book Sn,m = (n^2 + m^2) mod N (Page 316 of the Book), is still based on a prime number and is still not quite symmetrical. Cox and D'Antonio then go on to use PR sequences and the Chinese Remainder theorem to generate their 2D diffusers. But they don't dismiss the 2D QRD.

I am not saying that the 2D QRD is better than the Oliver 2D PRD design process, just that the QRDude 2D is still a real prime number diffuser, even though at first blush the design appears almost symmetrical.
Old 3rd February 2011
  #14
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jhbrandt's Avatar
Sebg,

Sorry, if I seem to ramble...
I was talking about single panels. Look at any of them...
to have a non-repeating diffusive surface, you would need all elements to be a different length.

A Prime-7 has only 4 different well depths including 0. Please tell me how many wells does your P7 QRD have? If it has more than 4, then something is repeating!

A Prime-23 QRD will have 11 different wells, then they repeat. - Usually mirror image (a mirror image is symmetrical - like many speaker driver layouts)

Yes, the QRDude 2D is a real prime number diffuser and it is very good. I was simply saying that the more perfect diffusion of a single sequence PRD has a better diffusion coefficient and zero lobbing. It's attenuation in the direction of the source is also much better.

Cheers,
John
Old 3rd February 2011
  #15
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Nordenstam's Avatar
 

The standard prime 7 QRD 0-1-4-2-2-4-1 sequence is perfectly symmetrical when implemented as 2-4-1-0-1-4-2. Ditto with the 2D QRDs, they can also be made to be fully symmetrical. (think there's a button for it in QRDude called "center" or similar)

The last applet on this page gives the 1D primitive root sequence for the least primitive root: Section 11.4: Quadratic Residues and Primitive Roots


John; I'm interested in why you think the diffusers should only span two octaves..? Why not three or four?


Andreas
Old 4th February 2011
  #16
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jhbrandt's Avatar
Quote:
Originally Posted by Lupo View Post
John; I'm interested in why you think the diffusers should only span two octaves..? Why not three or four?
Andreas,

Very good question.

Normal, natural sound diffusion that is experienced and understood by our brains usually covers the range of frequencies from 400Hz to around 6 to 8kHz. It is expected and 'feels' nice.

Above 6-8kHz, absorption by furniture and other wall treatment reduces the effect naturally & it is (in my opinion) a waste of time, energy, & money to create a diffusor that works much above 8kHZ.

Below about 400Hz, absorption is better applied to reduce the decay or ringing of modal & transition region frequencies. The boundaries of which depend on the room volume and absorption treatment applied.

I would suggest that if one is going to build a diffuser that has design bandwidth of 400Hz to 8kHz that they consider a diffractal type which has been proven to be very efficient at the broader bandwidth.

As I said before, I believe that the diffusor should be chosen for it's application.

Well, that's my story... and I'm stickin' to it.

Cheers,
John
Old 4th February 2011
  #17
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Jens Eklund's Avatar
Quote:
Originally Posted by jhbrandt View Post
Andreas,
I would suggest that if one is going to build a diffuser that has design bandwidth of 400Hz to 8kHz that they consider a diffractal type which has been proven to be very efficient at the broader bandwidth.
Agreed that diffractals are effective but there are other shapes that perform very well from 400 Hz to 8 kHz. Perhaps not within reach for the average Joe since you need BEM-modeling to find them, but still.

Sincerely Jens Eklund
Old 10th February 2011
  #18
Gear interested
 

Quote:
Originally Posted by jhbrandt View Post
When designing a custom diffusor for a particular room it is important to determine the regions of sound for that room. For example; a room that has the dimensions H = 350cm (320.9"), W = 560cm (220.5"), and D = 815cm (137.8") that is treated so that the averaged decay is about 0.4 sec. (RT-60) will have the following regions:
F1. (low frequency cut-off) = 21.09Hz
F2. (beginning of transition/diffusive region) = 94.73Hz
F3. (beginning of Ray region) = 378.91Hz
F4. (high frequency cut-off) = 20kHz ** sound does not cut off, but our attention does.

The diffusor recommendation for this room would be for a diffusor that has a design goal bandwidth from 756Hz to 3kHz. This diffusor would effectively cover the spectrum from 378.9Hz through to 9kHz - & that's plenty!

For a better understanding of the relationship of well width and diffusor depth get a copy of "Acoustic Absorbers and Diffusers" by Trevor J. Cox and Peter D’Antonio. Good luck!

Cheers,
John
John,
Why would you not design the diffuser to cover the transition/diffusive region? What is going on in this region that is different than the modal region or the ray region? Does Acoustic Absorbers and Diffusers cover the different regions of sound or is there another good source to get a better understanding of how the different regions behave?
Old 10th February 2011
  #19
SAC
Registered User
 

Quote:
Originally Posted by ryanred View Post
John,
Why would you not design the diffuser to cover the transition/diffusive region? What is going on in this region that is different than the modal region or the ray region?
Two factors:

Size due to the length of the wavelengths at issue.

Levels. If one is 'constructing' an ISD gap, you want all returned energy at least 20 dB SPL and ideally 30+ dB SPL, down relative to the direct arriving signal.
Old 10th February 2011
  #20
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avare's Avatar
 

Quote:
Originally Posted by ryanred View Post
John,
Why would you not design the diffuser to cover the transition/diffusive region? What is going on in this region that is different than the modal region or the ray region?
The modes are so infrequent that statistical acoustics is no longer valid.

Andre
Old 11th February 2011
  #21
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jhbrandt's Avatar
Thank you SAC & Andre. +1

- John
Old 11th February 2011
  #22
Gear interested
 

Thanks for the responses guys, I still have a couple questions:

Quote:
Originally Posted by SAC View Post
Levels. If one is 'constructing' an ISD gap, you want all returned energy at least 20 dB SPL and ideally 30+ dB SPL, down relative to the direct arriving signal.

I understand the concept of the ISD gap. I can see how your statement applies to determining whether or not a diffuser is appropriate treatment in the first place, but in what way does it apply to the range that the diffuser covers?

Quote:
Originally Posted by avare View Post
The modes are so infrequent that statistical acoustics is no longer valid.
Aren't the modes MORE frequent in this range or am I misunderstanding something?
Old 11th February 2011
  #23
SAC
Registered User
 

Quote:
Originally Posted by ryanred View Post
I understand the concept of the ISD gap. I can see how your statement applies to determining whether or not a diffuser is appropriate treatment in the first place, but in what way does it apply to the range that the diffuser covers?
.... because absorption ideally does not return energy to the region defined within the ISD gap and diffusion diffuses and returns diffuse energy at lower levels that may exceed the limits defined by the ISD.

Reviewing the definition and purpose of the ISD gap (and how it functions psycho-acoustically) may help clarify this further for you - as the definition encompasses all specular energy returns during this time period - regardless of frequency. (An excellent source for this is Sound System Engineering by Davis and Davis 2nd ed., or the 3rd ed. by Davis and Patronis.


You are still thinking in terms of frequency when the issue is defined in terms of energy and time - in the time domain.
Old 11th February 2011
  #24
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avare's Avatar
 

SAC is handling the other question in the post excellently.
Quote:
Originally Posted by ryanred View Post
Aren't the modes MORE frequent in this range or am I misunderstanding something?
Modes build up with increase in frequency. What is normally thought of as reverberation, or in relatively damped spaces as well balanced decay, is actually the range where the modes are occuring so often that modes combine with each other creating a general sound field. That is as opposed to the frequency ranges where the individual modes are apparent in the decay and frequency graphs.

This ties in with the usual cutoff for the room being considered as being where there are 3 modes per Hertz. This frequency is what is commonly refered to as the Schroeder frequency.

Yes, it was developed by same Manfred Schroeder who did the pioneering work on mathematically based diffuers.

Balanced and well diffused,
Andre
Old 11th February 2011
  #25
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Thanks again, I'll pick up Sound System Engineering soon.
Old 11th February 2011
  #26
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johndykstra's Avatar
 

Quote:
Originally Posted by SAC View Post
.... because absorption ideally does not return energy to the region defined within the ISD gap and diffusion diffuses and returns diffuse energy at lower levels that may exceed the limits defined by the ISD.

Reviewing the definition and purpose of the ISD gap (and how it functions psycho-acoustically) may help clarify this further for you - as the definition encompasses all specular energy returns during this time period - regardless of frequency. (An excellent source for this is Sound System Engineering by Davis and Davis 2nd ed., or the 3rd ed. by Davis and Patronis.


You are still thinking in terms of frequency when the issue is defined in terms of energy and time - in the time domain.
Is this to say then, that if one were to attempt to diffuse the transition frequencies, that the ISD termination would be too strong?
Old 12th February 2011
  #27
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jhbrandt's Avatar
Quote:
Originally Posted by avare View Post
Modes build up with increase in frequency. What is normally thought of as reverberation, or in relatively damped spaces as well balanced decay, is actually the range where the modes are occuring so often that modes combine with each other creating a general sound field. That is as opposed to the frequency ranges where the individual modes are apparent in the decay and frequency graphs.

This ties in with the usual cutoff for the room being considered as being where there are 3 modes per Hertz. This frequency is what is commonly refered to as the Schroeder frequency.
Very, very well said!

- John
Old 12th February 2011
  #28
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Nordenstam's Avatar
 

Quote:
Originally Posted by jhbrandt View Post
As I said before, I believe that the diffusor should be chosen for it's application.
Agreed.

Though I don't grasp the reason for avoiding the transition region from modal to specular behaviour. It's a region, not a cutoff.

Psychoacoustically, spatial clues in the sub 1000 Hz range seems to be very important. It seems to me that diffusers covering the range from somewhere in the transition region and up would be the best choice.
Old 12th February 2011
  #29
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jhbrandt's Avatar
Quote:
Originally Posted by Lupo View Post
Agreed.

Though I don't grasp the reason for avoiding the transition region from modal to specular behaviour. It's a region, not a cutoff.

Psychoacoustically, spatial clues in the sub 1000 Hz range seems to be very important. It seems to me that diffusers covering the range from somewhere in the transition region and up would be the best choice.
I don't think that I said anything about avoiding the transition region for diffusion, it is just that it becomes more and more difficult to diffuse the longer wavelengths - especially in small rooms such as we deal with in the average recording studio control room.

In my experience, I have found it adequate to apply diffusion down to about the mid-point of the transition region - and as I said before, this varies with room volume and trapping applied. I tried to show this on my Room Mode Calculator. You can scroll down a bit to see the regions & enter a decay time (RT-60). You will notice the change in the regional frequency range as you change the decay parameter.

Cheers,
John
Old 12th February 2011
  #30
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avare's Avatar
 

Quote:
Originally Posted by jhbrandt View Post
I don't think that I said anything about avoiding the transition region for diffusion, it is just that it becomes more and more difficult to diffuse the longer wavelengths - especially in small rooms such as we deal with in the average recording studio control room.
+1. Well worded. thumbsup

One of the factors being overlooked in this sub-topic in this thread is that in control applications, the goal is even dispersion. Close to diffusers, the listener is still in the pressure zone and strong lobing from the individual wells is present.

The usual rule of thumb is to be at least three wavelengths away from the pase grating type diffuser to avoid these effects. For 200 Hz even response this would mean being 15 feet away from the diffuser. Not very practical in home type control rooms. If one takes 300 Hz as the lowest frequency at which dispersion is desired, then the origin of the 10 foot guideline is self evident.

Andre
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