Consider a rigid plane in X-Y with the plane surface being defined as z= d*(1+sin(k*x)) where k is omega/c and d is < lambda. A wave incident on this obliquely will have an interesting reflection pattern especially with frequency and angle. It will be far from specular or diffuse. But if one compiled enough frequency points (2^n) spaced linearly one could synthesize a reflection grating to whatever specs one wanted using Fourier techniques.
Just an idea. Would make for a great publication (unless it's already been done - always a possibility.)
For a flat plane, if the reflection of an incident wave is called specular - it outputs the incident wave shape exactly in a near singular direction. In specular we have the classic, "angle out is equal to angle in". If the wave is scattered equally in all directions then this is diffuse. Neither completely exists in the field.
Now consider a pleated steel roof piece - typical construction material. It's surface could be described by the above equation,
The wave pattern of the reflecting surface will do very strange things to the reflection in the plane normal to the wave pattern on the reflector. If one had this spectral (polar) information at various frequencies, then one could calculate what the surface wave shape would be that would optimize its diffusion over any (well not "any") given bandwidth - even design in nulls.
This would be a lot like Schroeder's block approach, but with sines (he used integers.) More accurate I would think, than Schroeder's because of his simplifying assumptions.
Now consider a pleated steel roof piece - typical construction material. It's surface could be described by the above equation,
The wave pattern of the reflecting surface will do very strange things to the reflection in the plane normal to the wave pattern on the reflector. If one had this spectral (polar) information at various frequencies, then one could calculate what the surface wave shape would be that would optimize its diffusion over any (well not "any") given bandwidth - even design in nulls.
This would be a lot like Schroeder's block approach, but with sines (he used integers.) More accurate I would think, than Schroeder's because of his simplifying assumptions.
This sound a lot like phased array radar. Some have a lot of sources, but I think there is also a version that uses reflection of a surface with phase shifters in order to shape and steer the radar beam.
Edit: https://issuu.com/edrmag/docs/edr_49_-_web/s/10169591 Second section about the Pharos.
Edit: https://issuu.com/edrmag/docs/edr_49_-_web/s/10169591 Second section about the Pharos.
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Lets say I was trying to stay away from using a slot at the moment... Do you think the Axi could pull a >500hz XO with a OSWG?
This is the horizontal we are possibly looking at in regards to the woofer.
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Phased array sources are well known and easily calculated. I was doing them back in the 70's for sonar arrays. But this is a reflection - no sources - BIG difference.
Getting the reflection patterns should not be difficult. I only can't imagine what next. Don't the Fourier techniques require some orthogonal system as the basis? How would you check that / how is it even defined in this case? (I assume the amplitudes of the sines would be the searched coefficients.)
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Reflection could be a big difference. Conceptually I don't see why, mathematics may be more difficult. I don't know.
Reflectarrays are actually being used as indicated in my previous post. And I also found this:
Basically that is correct, but it doesn't really matter. Having the data at several frequencies one could just least squares fit the data and then orthogonality is not required.
That's a 2D idea, but to me a 1D would be more usable since horizontal is where one wants the reflection dispersed.
Do you have a 3d printer?
If you do - make the example plug mabat posted some pages back.
It will give you loading and HF directivity, and the price is a dip at 11khz on axis that nobody will hear.
You won't have any issues running the 2050 down to 400 at home levels.
All right. As you explicitly mentioned "Fourier techniques", I was only interested how would you do that...
OK, I get the gist and can try something, that's not a problem, I would only need some description of the simulation setup as a whole. I would use an axisymmetric layout if possible (either infinite baffle or free space). How large should be the "sine panel", what should be the source (point or plane), at what distance, position, etc. - a simple sketch would help. Then I would prepare the sims, which should be the easy part.
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If you're referring to the BEM part of Akabak, then technically yes, reflections from a surface can be modeled - especially at lower frequencies.
Although both BEM and FEA solve the linear wave equation in the frequency domain using a derivation of the Helmholtz integral. If you want to solve in the time domain, then you need to use COMSOL and the discontinuous-Galerkin method.
AFMG's Reflex and SoundFlow programs use a variety of 2D BEM to model scattering and sound transmission respectively.
https://www.afmg.eu/en/afmg-reflex
Diffuse scattering/reflection is a difficult problem, even at top-tier FEA levels. Impedance boundary conditions can be applied (or even modeled in full multi-physics) but the reflections are modeled as specular. You'd have to 'fake it' with mesh density if you wanted a lot of 'waves' generated from a normal velocity boundary driving condition.
If you’d like to make a test case, it might be useful to have comparison data. There’s a good example of measuring scattering coefficients to the ISO standard, for a pleated surface using a scale model of the material and a small reverb chamber here:
https://www.odeon.dk/pdf/ODEON and scattering.pdf
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I thought that Fourier might apply, but I wasn't sure. I still think that it would, since least-squares would certainly apply, why bother with Fourier unless speed is a requirement. After all Fourier is a least square approach.
The plane is thought to be infinite and the edges will have an effect so as large as practicable. The usual wavefront is plane because analytically that is easiest to deal with. Since it's a plane wave, distance can be anything, it doesn't matter. Normal incidence is not as interesting as oblique. The oblique angle for a test is not important, say 45 degrees. In the end what would be required is several angles from 0 to say 80 degrees.
I am not clear exactly how one would set up a numerical sim for plane waves. Perhaps you have some idea.
This program looks like it will do exactly what I want, but it's cost is too much for a simple DIY question.
In principle, you should be able to generate a similar model in Akabak3’s 2D BEM domain. It’s certainly free to download and try out, and 2D models solve fasteven on a laptop.
Any boundary can be set to axially vibrating with a simple velocity or acceleration, but the generated wavefront will be a function of the geometry dimensions. No reason why a flat plane couldn’t be used, but the size of it will limit the frequency range of validity for the model; just as a plane wave tube is limited by its own dimensions.
Afmg also offers a full-featured 30-day trial of Reflex, if you think that’s long enough to explore your concept. I’d not see a problem with using the trial to develop something if you’re not going to profit from it.
If I understand what you’re wanting to experiment with, this is a good example of a visually appealing but also very functional diffuser:
https://artnovion.com/product-categories/6-absorption/products/317-avalon-flow
A couple of comments.
A plane wave reflecting off of a rigid boundary cannot be represented by any distribution of velocity or acceleration of the boundary - it is rigid!
The link shows some designs that are mostly aesthetic with some absorption. The absorption is high at HFs and low at LFs - exactly the opposite of what I want. Those panel will have almost no diffusion at all. Not even close to what I am talking about.
A plane wave reflecting off of a rigid boundary cannot be represented by any distribution of velocity or acceleration of the boundary - it is rigid!
The link shows some designs that are mostly aesthetic with some absorption. The absorption is high at HFs and low at LFs - exactly the opposite of what I want. Those panel will have almost no diffusion at all. Not even close to what I am talking about.