The book has a entire chapter on waveguides. You can buy the book or go to Geddes on Audio and down load the pdfs for free.
The papers and preprints are all available from the AES as single copies, but you would have to pay for them. Otherwise go to the library.
I see rectangular waveguides as a bad choice since all compression drivers have circular apertures. There will always be a problem going from round to rectangular. There is no good way to do that. Circular to elliptical is doable (I have waveguides that do that), but not circular to rectangular. That's why I never pursued rectangular waveguides.
There are elliptical solutions as well, they are called Neumann Functions and the same techniques used for the conical spherical can be done in the elliptical case. There are FORTRAN routines that calculate these elliptical functions. I don't know about C++.
I have tried that before, I did not find any good solutions. Cars are not good places for good audio systems.
Recent studies that I have seen found that the difference between a "normal" car audio system and a optional Hi-end audio system are shrinking to the point of very small advantage for the Hi-end systems. Not what Bose or Harman marketing want you to think but something that the car companies are coming to realize. There is not much room in a car for a real product differentiation based on performance. These systems are becoming a commodity.
Recent studies that I have seen found that the difference between a "normal" car audio system and a optional Hi-end audio system are shrinking to the point of very small advantage for the Hi-end systems. Not what Bose or Harman marketing want you to think but something that the car companies are coming to realize. There is not much room in a car for a real product differentiation based on performance. These systems are becoming a commodity.
Earl,
thank you for the fact you have your book as pdf files on your website. I rather like real books so I am sure I will buy the book here at some point, I don't particularly like reading on a computer screen and it is nice to be able to change pages at will. The cost to print the book on my printer would probably not save much at the cost of ink cartridges and they just aren't the same as a bound book.
In your preprints and AES Journal papers is there information that would not be in your book, or is it all inclusive?
thank you for the fact you have your book as pdf files on your website. I rather like real books so I am sure I will buy the book here at some point, I don't particularly like reading on a computer screen and it is nice to be able to change pages at will. The cost to print the book on my printer would probably not save much at the cost of ink cartridges and they just aren't the same as a bound book.
In your preprints and AES Journal papers is there information that would not be in your book, or is it all inclusive?
Chapter 6 in my book is IMO the most complete coverage on waveguides that I know of in one place. Start there and if you need more information then go for the papers.
Earl,
I am not so sure that you can not create a mathematical method of shape changing from a round cross section to a rectangular one, but the real question would become why would anyone want to do that on purpose? It is not a shape that a waveform is going to want to follow or remain attached to, the corners and parallel sides are going to be a problem, that has always been the failing of radial horns using classical designs. The break point where the throat and the angular flare join is always a compromised solution and this is what I think led us both down the path we both have taken. There is no mathematical solution to that conjunction of the throat and flare in a standard radial horn, this is going to be a major creator of your homs distortion from what I have just started to look at from your work. I don't understand why people can not see the correlation between this and fluid dynamics and shape changes?
I am not so sure that you can not create a mathematical method of shape changing from a round cross section to a rectangular one, but the real question would become why would anyone want to do that on purpose? It is not a shape that a waveform is going to want to follow or remain attached to, the corners and parallel sides are going to be a problem, that has always been the failing of radial horns using classical designs. The break point where the throat and the angular flare join is always a compromised solution and this is what I think led us both down the path we both have taken. There is no mathematical solution to that conjunction of the throat and flare in a standard radial horn, this is going to be a major creator of your homs distortion from what I have just started to look at from your work. I don't understand why people can not see the correlation between this and fluid dynamics and shape changes?
Earl,
Even if you used a device that would go from a round diaphragm to a square exit phase plug aren't we just moving the diffraction point farther back into the device and creating the exact same problems that we would if doing this in the waveguide itself? I don't see the advantage to this except that the diffraction would happen at a higher frequency point in time rather than farther down the waveguide where the waveforms would be at a large scale and lower frequency?
Even if you used a device that would go from a round diaphragm to a square exit phase plug aren't we just moving the diffraction point farther back into the device and creating the exact same problems that we would if doing this in the waveguide itself? I don't see the advantage to this except that the diffraction would happen at a higher frequency point in time rather than farther down the waveguide where the waveforms would be at a large scale and lower frequency?
Pano,
No matter how you cut it square or rectangular you have created many problems that have no solution really. Parallel walls and corners where the waveform will be forced to detach. There is no solution for that. The waveguides that I have worked to develop never have any parallel walls and never have a square corner. This is one of the reasons that I find so much fault with the multicell horns you so love. I know in the original theory it seemed like a good solution it was just another band aid. If you used multiple oblate spheroids that joined at the mouth cutoff frequency you would be way ahead of the game with a multicell waveguide. There is no way around the problems caused by rectangular cross sections which by the way includes square as a subset of rectangular.
No matter how you cut it square or rectangular you have created many problems that have no solution really. Parallel walls and corners where the waveform will be forced to detach. There is no solution for that. The waveguides that I have worked to develop never have any parallel walls and never have a square corner. This is one of the reasons that I find so much fault with the multicell horns you so love. I know in the original theory it seemed like a good solution it was just another band aid. If you used multiple oblate spheroids that joined at the mouth cutoff frequency you would be way ahead of the game with a multicell waveguide. There is no way around the problems caused by rectangular cross sections which by the way includes square as a subset of rectangular.
Square - rectangle, completely synonymous, except that a high aspect rectangle would be even worse.
No actually it is possible to go from an annular slit at the diaphragm to a square aperture without diffraction. This is what my patent is about. But once the annuli have been combined into a circle then it can't be squared again with diffraction at the edges.
Thanks, makes perfect sense.
At one time I had begun building a honeycomb multi-cell horn. Actually it was more of a soccer ball face than pure honeycomb. (see below) Still, many of the sections had parallel walls. It would have made a nice section of a sphere, and that was the point. I was saved from the tedium by a good price on some used Altec horns.
I think that an oval or round mouth multi-cell would be interesting, but what does one do with the spaces between the mouths where they don't touch?
FWIW, two of the most amazing, cleanest horns I've ever heard are rectangular - the WE-15A and its little brother the Vitaphone 11A. But of course they have the luxury of going from round to rectangle over a throat distance that is longer than the total length of many other horns.
Attachments
But why go to rectangular at all - I don't see any advantages. Some quote a larger mouth area, but really what's the advantage in that? It the distance across the mouth that matter not the area. I don't see where the area enters into the problem at all.