Heating of the surroundings causing thermal distortion of the air will do this too. Bloody kills the high end, voices garbled, yuck
Now come on Tom, you know we all love 901's 😀
From the charts, both the H9800 and most of the PT waveguides are pretty smooth. Those PT waveguides are pretty good parts.
I personally have found that most waveguides aren't quite as smooth as exponential horns, on-axis, but what they lose in the trade they make back in polars. And this is only for the horns with approximately 90° beamwidth. As the pattern is narrowed, the catenary horns can become easily as smooth as the exponentials, and they have the benefit of constant directivity so narrower catenary horns are more of a no-brainer.
In fact, as I remember there was a researcher in the past that did some work for the military, and he found catenary horns to present an even better acoustic load than exponentials. Seems like he worked out a way to make it fit the Webster equation. I've slept since then so I don't remember all the details but I do remember it was interesting that in certain configurations, the catenary horn can provide even better acoustic loading than an exponential, and therefore can provide smoother response.
There was another guy in the 1950s that built catenary basshorns, but I sort of disregarded that because it's a different animal. But the academic papers in the 1950s and the military work in the 1970s was pretty interesting stuff. And of course there is Geddes work in the last decade or two. Do a search for "catenoidal horn" and read through the links. I remember digging through for months back around 2001/2002. Gotta be even more about them available now.
To me, it's all a balance. To get the smoothness, we need one flair profile, but to get the directivity, we need another. But the right catenary promises to do both. That's the sweet spot, in my opinion.
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I guess this was kind of overlooked, maybe partially 'cause it is a little off-topic. But I do find it related, and very interesting.
We were talking about waveguide flare shapes in the "JBL horn" thread, and it got me on a tangent, remembering way back when I first started looking at the Hughes quadratic throat waveguide.
That was the first commercially available waveguide I am aware of. I started using Peavey horns back then, in some models of my speakers. My own H290C waveguide is much like the Peavey waveguide, for that matter, except mine uses a true catenary flare, not the "quadratic" radius used in throat of the Hughes/Peavey waveguide.
But I digress. Where I was going was the catenary flare profile, and how it is actually a fairly old shape for acoustic horns. The recent attention given to it by oblate spheroid waveguides and other similar waveguide shapes is new, but the catenoidal horn itself is not new to audio. It was used in the 1950s as a basshorn, and in later years became useful for ultrasonics applications and even military applications, mostly for sonar.
After I became attracted to the Quadratric Throat waveguide - much because of its smooth features and its resemblance to radial horns - I found myself on the road to learning about Earl Geddes and his infatuation with the catenoid. He called it an Oblate Spheroidal waveguide, because that's the coordinate system it's based on. Others are Prolate Spheroid and Elliptic Cylinder. But the basic curve is the catenary, and when rotated about its directix, it becomes a catenoid. This is a minimal surface, much like a naturally occuring bubble.
When I started learning about Geddes approach - to use a catenoid as a waveguide - I saw that it was very similar to the Hughes waveguide. In fact, Earl says he consulted with Hughes and that the Geddes catenary waveguide preceded the Hughes waveguide, it just didn't get any attention at first. So but the fact remained that the catenoid Geddes promoted was similar to the quadratic shape Peavey used, and the catenoid being a mimimum surface seemed "intuitively right" to me. So I began to research it in more detail.
That's when I found out that it was actually a pretty old shape for acoustic horns, and that ironically, it was used first as a basshorn. When the catenoid is long and thin, it provides strong acoustic loading. It is only when it is opened wider, as is more useful for HF waveguides, does it take on a shape that acts more like a conical horn. So that always stuck in my mind as a useful fact, one that might guide me towards a smooth sounding horn that also provides nearly constant directivity.
Again, I would suggest to anyone that is interested in acoustic horns and waveguides, study the older material on catenoidal horns along with the newer claims that have been made about this waveguide/horn flare. It is a very interesting shape.
We were talking about waveguide flare shapes in the "JBL horn" thread, and it got me on a tangent, remembering way back when I first started looking at the Hughes quadratic throat waveguide.
That was the first commercially available waveguide I am aware of. I started using Peavey horns back then, in some models of my speakers. My own H290C waveguide is much like the Peavey waveguide, for that matter, except mine uses a true catenary flare, not the "quadratic" radius used in throat of the Hughes/Peavey waveguide.
But I digress. Where I was going was the catenary flare profile, and how it is actually a fairly old shape for acoustic horns. The recent attention given to it by oblate spheroid waveguides and other similar waveguide shapes is new, but the catenoidal horn itself is not new to audio. It was used in the 1950s as a basshorn, and in later years became useful for ultrasonics applications and even military applications, mostly for sonar.
After I became attracted to the Quadratric Throat waveguide - much because of its smooth features and its resemblance to radial horns - I found myself on the road to learning about Earl Geddes and his infatuation with the catenoid. He called it an Oblate Spheroidal waveguide, because that's the coordinate system it's based on. Others are Prolate Spheroid and Elliptic Cylinder. But the basic curve is the catenary, and when rotated about its directix, it becomes a catenoid. This is a minimal surface, much like a naturally occuring bubble.
When I started learning about Geddes approach - to use a catenoid as a waveguide - I saw that it was very similar to the Hughes waveguide. In fact, Earl says he consulted with Hughes and that the Geddes catenary waveguide preceded the Hughes waveguide, it just didn't get any attention at first. So but the fact remained that the catenoid Geddes promoted was similar to the quadratic shape Peavey used, and the catenoid being a mimimum surface seemed "intuitively right" to me. So I began to research it in more detail.
That's when I found out that it was actually a pretty old shape for acoustic horns, and that ironically, it was used first as a basshorn. When the catenoid is long and thin, it provides strong acoustic loading. It is only when it is opened wider, as is more useful for HF waveguides, does it take on a shape that acts more like a conical horn. So that always stuck in my mind as a useful fact, one that might guide me towards a smooth sounding horn that also provides nearly constant directivity.
Again, I would suggest to anyone that is interested in acoustic horns and waveguides, study the older material on catenoidal horns along with the newer claims that have been made about this waveguide/horn flare. It is a very interesting shape.
Wayne,
You can make up any names you want but as you say there are truly no real shapes that were not investigated somewhere in the past going back to Webster. What has really happened are that new manufacturing methods allowed shapes to be produced that just weren't practical in the past, wood is limited in mass production with what you can do and the same goes for aluminum in the past due to the difficulty with the tooling for sand casting or die casting. Where we are today is a manipulation of the shapes while following the expansion rates that are dictated by the differing expansion topologies. Obviously conic sections are the simplest to produce but do require extensive eq to create a flat response.
You can make up any names you want but as you say there are truly no real shapes that were not investigated somewhere in the past going back to Webster. What has really happened are that new manufacturing methods allowed shapes to be produced that just weren't practical in the past, wood is limited in mass production with what you can do and the same goes for aluminum in the past due to the difficulty with the tooling for sand casting or die casting. Where we are today is a manipulation of the shapes while following the expansion rates that are dictated by the differing expansion topologies. Obviously conic sections are the simplest to produce but do require extensive eq to create a flat response.
The Peavey was not the first use. In 1990 I worked with Adamson Acoustics and we made a commercial product almost six years before Peavey.
Charley Hughes got in touch with me because he had read my 1991 paper on the subject.
About a year AFTER I went to Meridian and taught Charley about them, Peavey came out with the Quadratic one. That was probably 1995-96.
I have never seen a reference to any catenoid waveguide prior to the 1951 paper by Freehafer. Stratman, Freehafer's advisor, was into radar at MIT's Lincoln Lab and wrote the book on the wave equation in spheroidal coordinates in 1953. That laid the groundwork for derivations of these devices for Sonar and Radar, but this is much much later than what you are quoting. The first, to my knowledge, solution to the wave equation in spheroidal coordinates was in Morse and Feshbach from the late 40's.
The reason that this is not true is that the OS waveguide slope is a two term equation. Webster's approach cannot handle two term equations so no two-term shape has ever been done using Webster. Try and solve Webster's equation with any two term slope. There is never a nice closed form solution like we can always find for a single term slope.
Earl,
I don't want to argue with you and yes you are probably correct that in the printed literature there was not a more complex form of the equation printed. But to say that somebody even then could not produce a two term equation is just not so. I think that many mathematicians have done things that never see the light of day, on that I think we can agree. There are things that Paul Klipsh wrote of that never saw the light of day as he didn't have a way to manufacture them using wood. Doesn't mean people haven't thought of this stuff before. Just never made it to paper to be presented to others. I can site one of your patents but don't know the patent number where you do discuss different compression driver shape changes which I have also thought about, but I have not seen you commercialize them. They would not be a universal fit to anyone else horn or waveguide, but I still think it is a great idea if they were produced. Unless you read that patent paper someone would think nobody else ever thought of that.
I don't want to argue with you and yes you are probably correct that in the printed literature there was not a more complex form of the equation printed. But to say that somebody even then could not produce a two term equation is just not so. I think that many mathematicians have done things that never see the light of day, on that I think we can agree. There are things that Paul Klipsh wrote of that never saw the light of day as he didn't have a way to manufacture them using wood. Doesn't mean people haven't thought of this stuff before. Just never made it to paper to be presented to others. I can site one of your patents but don't know the patent number where you do discuss different compression driver shape changes which I have also thought about, but I have not seen you commercialize them. They would not be a universal fit to anyone else horn or waveguide, but I still think it is a great idea if they were produced. Unless you read that patent paper someone would think nobody else ever thought of that.
I find the catenary to be an interesting shape, and very useful for horns. But after seeing the way the oblate spheroidal waveguide was described in the 2000s (and still today), I guess I was surprised to find out that it was seen much like all other Salmon shapes in the past, not as something new and unique.
The horn contour described by the hyperbolic cosine in Salmon’s paper was later called a catenoid by Morse in his book, "Vibration and Sound". Since a hyperbolic cosine describes a catenary curve, and since a revolution of the catenary on its directix produces a catenoidal surface, the Oblate Sheroidal waveguide is actually a Salmon family horn, one that can be described by the Webster equation.
Of course, none of that discounts the whole idea of high-order modes or of the reality that wavefront propogation isn't one-dimensional. I think it is more than reasonable to make the case that the one-dimensional Webster approximation is just that - an approximation - and to bring into sharp focus the fact that reality isn't one-dimenisional, and neither is the wavefront propogation. In fact, that's the whole point, getting the plane wave to expand into a spherical section smoothly.
Still, I do find some of these other academic sources to be useful, and their findings are interesting to me. And I absolutely do not dismiss the importance of acoustic impedance or horn loading. It is one thing to say sound waves move in three dimensions, so a one-dimensional approximation is incomplete. It is another thing entirely to dismiss the notion or importance of acoustic loading just because the formulas commonly used to calculate it are approximations. I think they are extremely useful approximations, especially since they happen to do a pretty good job of predicting acoustic impedance.
Very cool. I wasn't aware of the Adamson horn. First I heard was the Peavey waveguide, but it did set me on the road to finding yours.
I was simply surprised to find any work on catenoids back prior to the 1970s, and found quite a bit of prior work.
I can see what you're saying, I think, basically that the Webster equation is an approximation. If that is what you are saying, then I agree. But I do find numerous references of people using the Webster equation to solve for a catenoidal horn, which is what the Oblate Spheroidal waveguide is.
This is entirely incorrect, just as Kindhorn's comment are incorrect. One CANNOT solve the OS waveguide with Webster's equation - try it. I did and I was not able to solve it and I am no slouch at math. Webster's equation is an approximation yes, but the OS waveguide is exact. This is not some small difference. Webster's equation is a dead end if one wants to look at directivity of a waveguide. The OS solution is not and, to repeat, it cannot be solved with Webster's approach.
The fact that one can find catenoids for which Websters equation does works does not mean that it will work for all catenoids.
I have no problems with you guys trying to hypothesize about how horns work, but when you make statements that are just plane wrong I am going to call you on it.
Kindhornman - I find it ridiculous to believe that because something could have been done that it has been done. By that logic all that could ever be done already has been done. We only know that something has been done if there is evidence to that fact. Lacking any evidence it must be assumed that it has not been done.
I remember finding numerous scholarly articles about solving catenoidal horns with Webster's equation. I don't think it would be any trouble to find specific examples, any Google search would probably turn up several. Then again, as I recall, the ones I'm thinking of weren't concerned with directivity, but of acoustic impedance.
Like I said earlier, the OS waveguide is a catenoid, and that is a Salmon family horn. You may not approve of the quality of its approximation, since it requires a plane wave to be accurate. I would agree with you, especially in the case of a "wide mouth" catenoid. But still, it is a hyperbolic cosine, a catenoid, which is described in Salmon's paper.
Honestly, I think that's probably true. I expect that the Webster equation would be much more accurate on long, thin catenoids than wider open ones, simply because the wavefront expands less. It's more like a planar wave throughout.
But I think it is important to point out that the OS waveguide is a catenoidal horn. They are the same thing. That way when hobbyists do research, they will find all the information available. There is a lot of work on catenoidal horns.
Please post them. Its your claim to prove not mine.
You keep repeating this so I will keep repeating that it is incorrect. Salmon's family of horns are all one-term forms and the OS waveguide is not. They are completely different. The OS waveguide is NOT a Hyperbolic Cosine.
Wayne - you keep saying things that are incorrect and claiming that there is a lot of literature, then provide some. I have studied this problem in far more depth than you have and I am saying that your claims are wrong.
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Earl,
I would never argue with you over your math, that would be stupid on my account. I wonder though why if your solution is so good at predicting and controlling dispersion it has not become the dominant shape for waveguides. I still will maintain that there are other solutions and other implementation that can be used to solve the same problem. I am not saying they are superior, perhaps just different and in other instances may be used instead of the OS waveguide design.
I would never argue with you over your math, that would be stupid on my account. I wonder though why if your solution is so good at predicting and controlling dispersion it has not become the dominant shape for waveguides. I still will maintain that there are other solutions and other implementation that can be used to solve the same problem. I am not saying they are superior, perhaps just different and in other instances may be used instead of the OS waveguide design.
Where are we miscommunicating here?
The OS waveguide is a catenoid. It is a catenary rotated about an axis. You have said so yourself on several occasions, when describing your waveguide. Has there been some kind of misunderstood all these years?
That said, catenoids are mentioned in several academic papers I've read over the years. Maybe you don't agree with these guys, I don't know. But I know there is modeling software that simulates response of horns like these, and that software must use the formula in the literature, no? I mean, you didn't license any of your own code to anyone, did you? So what formula do you suppose they are using?
You asked me to find academic papers about catenoids being described as Salmon family horns, but I wasn't aware that was in question. I mean, it's in several basic texts and even more papers of various sorts. Kinda not sure how to respond, because catenoidal horns are Salmon family horns. They're the case where m>0 and T=0. One example is Leach's horn modeling paper, where he uses Spice to create an analog. There, on page 2 he describes the catenoid case. There are so many other papers like this, it just doesn't make sense to list them all. But here's Leach's:
I dunno, Earl. Sometimes I get where you're coming from, but sometimes I just don't. I can buy the argument that a wide-mouthed catenary horn wouldn't follow the Webster approximation very well because the wavefront propogation isn't planar the closer to the mouth it gets. This likely follows with other horn shapes too. But a longer catenoidal horn with smaller mouth area probably does lend itself to approximation with Webster's equation. And in any case, the catenoidal horn shape is described as a Salmon family horn. Whether you want to argue Webster's validity, it is still listed as such, described by Salmon in what, 1946?
The OS waveguide is a catenoid. It is a catenary rotated about an axis. You have said so yourself on several occasions, when describing your waveguide. Has there been some kind of misunderstood all these years?
- "The Oblate Spheriodal waveguide is a catenoid..."
- "Interestingly enough the OS shell is also a catenoid of minimum surface..."
That said, catenoids are mentioned in several academic papers I've read over the years. Maybe you don't agree with these guys, I don't know. But I know there is modeling software that simulates response of horns like these, and that software must use the formula in the literature, no? I mean, you didn't license any of your own code to anyone, did you? So what formula do you suppose they are using?
You asked me to find academic papers about catenoids being described as Salmon family horns, but I wasn't aware that was in question. I mean, it's in several basic texts and even more papers of various sorts. Kinda not sure how to respond, because catenoidal horns are Salmon family horns. They're the case where m>0 and T=0. One example is Leach's horn modeling paper, where he uses Spice to create an analog. There, on page 2 he describes the catenoid case. There are so many other papers like this, it just doesn't make sense to list them all. But here's Leach's:
I dunno, Earl. Sometimes I get where you're coming from, but sometimes I just don't. I can buy the argument that a wide-mouthed catenary horn wouldn't follow the Webster approximation very well because the wavefront propogation isn't planar the closer to the mouth it gets. This likely follows with other horn shapes too. But a longer catenoidal horn with smaller mouth area probably does lend itself to approximation with Webster's equation. And in any case, the catenoidal horn shape is described as a Salmon family horn. Whether you want to argue Webster's validity, it is still listed as such, described by Salmon in what, 1946?
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It is.
You are completely off base here, but I'll leave it alone because I know how you get when people contradict you.
So do I.
There was a PhD thesis done in Australia where the guy used parametric BEM to find that shape of waveguide which yielded the most ideal directivity control. His answer was nearly identical to an OS waveguide, which I had predicted some 20 years earlier.
There is no better shape for directivity control. Sure there are plenty of other shapes and maybe some of them, like the quadratic waveguide, are almost as good, but somehow having someone give you the answer ahead of time always makes the problem easier.
Catenoid horns have been discussed for years, and modeled with the Webster equation. Whether or not that formula is perfect is not in question, we all agree that it is an approximation that depends on planar wave propogation. But there are a lot of useful formulas that are approximations.
This kind of reminds me of the Helmholtz formula to calculate cavity resonance. It depends on volume, port area and length, but the length has to be "fudged" with an area correction factor. Does that make it worthless? No, it's still useful.
Same thing with the Webster equation. Is it perfect, no. Is it useful, well, most acousticians seem to think so. In fact, I can't say I know anyone else in the world that dismisses the Webster equation so completely. Everyone knows it is a 1P approximation, and everyone knows that has limits. Some have proposed "fudge factors" for curved pipes and flares and other things that cause the 1P assumption to be wrong. They try to make the mathematical model better, which I think is a worthwhile effort. But it does still seem to be the most popular mathematical model for simulating horns and many other acoustic devices.
This kind of reminds me of the Helmholtz formula to calculate cavity resonance. It depends on volume, port area and length, but the length has to be "fudged" with an area correction factor. Does that make it worthless? No, it's still useful.
Same thing with the Webster equation. Is it perfect, no. Is it useful, well, most acousticians seem to think so. In fact, I can't say I know anyone else in the world that dismisses the Webster equation so completely. Everyone knows it is a 1P approximation, and everyone knows that has limits. Some have proposed "fudge factors" for curved pipes and flares and other things that cause the 1P assumption to be wrong. They try to make the mathematical model better, which I think is a worthwhile effort. But it does still seem to be the most popular mathematical model for simulating horns and many other acoustic devices.
More interesting are the results of modeling these so called 'useful' BR designs with TL software. Other than the golden ratio enclosure all others appear to be flawed until we get to the proper TL requirements.
Doing this was a real eye opener, explained a lot, especially the boominess (other than highish Q) and harmonic coloration common to BR designs
I took a minute this evening to grab some of the references I was talking about earlier. Some are probably new too, at least newer than those I had originally seen. But they are all germane to this discussion, which is the usefulness of the Webster equation, and the conditions that make it less accurate.
It isn't so much whether the catenoid is a Salmon shape or not - it is. When it is made to be long and thin, the Webster equation does an adequate job. The problem is when it is made short and wide, where the flare curves rapidly, because the wavefront is not close to being planar. This is not isolated to catenaries, it is a problem no matter what shape the flare profile is, and it is pretty well documented.
Various solutions have been proposed, some that are sort of adjustments to the Webster equation, others that are entirely new. Some try to "fit" the solution into the Webster equation or some lumped parameter model, others use BEM or another iterative technique. But all are looking at the problem of how to accurately model a horn (or duct or other similar acoustic device) when a one-dimensional approximation doesn't suffice. Here are papers about some of them:
It isn't so much whether the catenoid is a Salmon shape or not - it is. When it is made to be long and thin, the Webster equation does an adequate job. The problem is when it is made short and wide, where the flare curves rapidly, because the wavefront is not close to being planar. This is not isolated to catenaries, it is a problem no matter what shape the flare profile is, and it is pretty well documented.
Various solutions have been proposed, some that are sort of adjustments to the Webster equation, others that are entirely new. Some try to "fit" the solution into the Webster equation or some lumped parameter model, others use BEM or another iterative technique. But all are looking at the problem of how to accurately model a horn (or duct or other similar acoustic device) when a one-dimensional approximation doesn't suffice. Here are papers about some of them:
- A Modeling and Measurement Study of Acoustic Horns, John T. Post and Elmer L. Hixson
- Acoustical Klein-Gordon Equation: A Time-Independent Perturbation Analysis, Barbara J. Forbes and E. Roy Pike
- The Webster Equation Revisited, Sjoerd W. Rienstra
- Computer Simulation of the Acoustic Impedance of Modern Orchestral Horns, A. Benoit and J.P. Chick
- The horn-feed problem: sound waves in a tube joined to a cone, and related problems, P. A. Martin
- Input impedance computation for wind instruments based upon the Webster-Lokshin model with curvilinear abscissa, Thomas Hélie, Thomas Hézard and Rémi Mignot
- Comparisons between models and measurements of the input impedance of brass instruments bells, Pauline Eveno, René Caussé Ircam, Jean-Pierre Dalmont and Joël Gilbert
- Wave Propagation and Radiation in a Horn: Comparisons Between Models and Measurements, Pauline Eveno, René Caussé Ircam, Jean-Pierre Dalmont and Joël Gilbert
A lot of interesting stuff here as well as links. Thanks! The way I see it, admittingly with very limited knowledge about horn lenses, it finally boils down to choosing the best compromise for the spesific application.
Can anyone of you comment on the performance of a Klipsch K-402 and JBL 2360A horn.
K-402. From what I've read it's conical in the throat area with a tractrix mouth.
JBL 2360A bi-radial. http://www.jblpro.com/pub/obsolete/23606566.pdf
Can anyone of you comment on the performance of a Klipsch K-402 and JBL 2360A horn.
K-402. From what I've read it's conical in the throat area with a tractrix mouth.
JBL 2360A bi-radial. http://www.jblpro.com/pub/obsolete/23606566.pdf
Wayne
Those are all recent publication and have nothing to do with OSWG. Seems like you just grabbed some papers to try and support your claim, which remains unfounded.
Those are all recent publication and have nothing to do with OSWG. Seems like you just grabbed some papers to try and support your claim, which remains unfounded.
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