What claim is that? The claim that a catenoid is Salmon family? It is, we all know that it is. But we also know the Webster equation becomes less accurate when the flare opens wide. I think that's what you've been saying too, isn't it?
What I'm saying is I remember papers about solutions to that problem. Some are old, some are newer. Doesn't matter, there are tons of textbooks and other documents, both on the Salmon family (and the catenoid) and also on the conditions that push the Webster equation to the extreme. I suggested that people might be intersted in looking them up, and eventually posted links to some.
No it's not. "A catenoid", maybe, an OSWG, no. The fact that the bounding curve is a catenoid does not make it a Salmon horn. In fact Salmon never even used the term catenoid. It is shear coincidence if one of his curves turns out to be one and this in no way makes all catenoid curves "Salmon". In fact you are the only person who uses the term "catenoid horn" (I never heard it before you used it) as if it is something that is well understood. I mentioned to you once that the OSWG curve was a catenoid and now you have created this whole myth that these were all well understood for decades. It is simply not true.
Last edited:
Almost every paper I've read that describes Salmon family horns includes the catenoid shape. It's in basic textbooks too. That was one of the things that interested me, the fact that the waveguide flare profile was actually the same as a Salmon horn. The only difference I see is that the way we're using them is with much more open flares, not long and thin like Webster's equation needs for accuracy, because of the 1P condition. But a catenoid is descibed as a Salmon family horn, as are conical, exponential and hyperbolic.
Wayne,
Thanks for all the references. I have seen quite a few references to the catenoidal shape used in ultrasonics and also sonar applications.
Thanks for all the references. I have seen quite a few references to the catenoidal shape used in ultrasonics and also sonar applications.
"The" catenoid shape? There are an infinite number of catenoids, its a mathematical class of functions that define the shape of a functional under a set of minimization and end point constraints (do you actually know what those are for say an OSWG?). Salmon may use one of them, but he does not define them all. And, as I said, he never uses the word catenoid even if one of his functions is. So clearly this class of functions was not important to him.
You appear to be the only person using this phase in the context of horns and waveguides and trying to make it have some global meaning. That's fine, but you just can't wave your hands and make it happen. You have to support your claims with some actual mathematics.
This just keeps getting better and better.
Ok guys, show me a couple in refereed publications. Ones where the actual word is "catenoid" and not that the functions just may be a catenoid.
In fact every function is a catenoid under some set of conditions. That makes all horns and waveguides "catenoid horns".
With regard to the OSWG and directivity, I never thought that it was presumed to be the ultimate in that regard. I thought the design was meant to be a solution to higher order modes and to give good low end loading.
My understanding concerning directivity is that the straight sided conical waveguide with appropriate end flaring was/is the best solution for polar uniformity, it just tends to be bad for bottom end loading. Certainly the Keele Biradial versions are very good in both polar uniformity and d.i. uniformity. I don't know that you surpass them in those regards (I've never seen conventional beamwidth and d.i. plots for your product but would infer this from your color dispersion plots).
Any horn with a varying expansion rate and a continuosly flaring wall contour will have higher directivity at high frequencies, lower directivity at lower frequencies. This is a consequence of beamwidth being formed back in the horn at HF and more at the front for LF (that evil diffraction thing). This doesn't preclude, OS, Catenary, Tractrix or Exponential horns from having reasonably smooth directivity, but it does prevent them from having constant directivity.
I've mentioned before that a lot of things with smooth directivty these days are being called constant directivity. An arguement can be made that a gradually climbing directivity is a good thing in system design, but lets not call it constant directivity.
David
My understanding concerning directivity is that the straight sided conical waveguide with appropriate end flaring was/is the best solution for polar uniformity, it just tends to be bad for bottom end loading. Certainly the Keele Biradial versions are very good in both polar uniformity and d.i. uniformity. I don't know that you surpass them in those regards (I've never seen conventional beamwidth and d.i. plots for your product but would infer this from your color dispersion plots).
Any horn with a varying expansion rate and a continuosly flaring wall contour will have higher directivity at high frequencies, lower directivity at lower frequencies. This is a consequence of beamwidth being formed back in the horn at HF and more at the front for LF (that evil diffraction thing). This doesn't preclude, OS, Catenary, Tractrix or Exponential horns from having reasonably smooth directivity, but it does prevent them from having constant directivity.
I've mentioned before that a lot of things with smooth directivty these days are being called constant directivity. An arguement can be made that a gradually climbing directivity is a good thing in system design, but lets not call it constant directivity.
David
Earl,
I am not arguing with you about this, I only stated that I have seen the term used and specifically in those two applications. Its get to the argument of what hyperbolic value you use, they are still hyperbolic though some chose different values as their preferred exponent. You have chosen a specific value to describe your waveguides and I understand that. You have done your studies and determined a formula that gives the results you conclude are optimum, I have no qualms with that.
I am not arguing with you about this, I only stated that I have seen the term used and specifically in those two applications. Its get to the argument of what hyperbolic value you use, they are still hyperbolic though some chose different values as their preferred exponent. You have chosen a specific value to describe your waveguides and I understand that. You have done your studies and determined a formula that gives the results you conclude are optimum, I have no qualms with that.
I am baffled by what Wiki says about catenoids and catenaries. According to them there is only one shape that is a catenary - the OSWG is not a catenoid according to Wiki. I will have to figure out where I got that the OSWG is a catenary. As I understood it the OSWG shape is a catenary where the slopes at the end points are fixed and the shape is that which minimizes the gradient between the two points.
I understand what Wayne was saying now and why I disagreed with it, because I also disagree with Wiki. If the only shape that is a catenary is a hyperbolic cosine then the OSWG is NOT a catenary and hence not part of Salmons family as I have been saying all along. But if the definition of a catenary is more general than Wiki explains then the OSWG would be a catenary under a different set of constraints and there would thus be many catenaries.
he point here is that the OSWG is not part of any prior work in horns etc. that I had seen except the work that Salmon did comparing his horns to the Freehafer solution where it is very clear that he understood that the two were different.
I still challenge someone to show me "catenary horn" in the literature.
I understand what Wayne was saying now and why I disagreed with it, because I also disagree with Wiki. If the only shape that is a catenary is a hyperbolic cosine then the OSWG is NOT a catenary and hence not part of Salmons family as I have been saying all along. But if the definition of a catenary is more general than Wiki explains then the OSWG would be a catenary under a different set of constraints and there would thus be many catenaries.
he point here is that the OSWG is not part of any prior work in horns etc. that I had seen except the work that Salmon did comparing his horns to the Freehafer solution where it is very clear that he understood that the two were different.
I still challenge someone to show me "catenary horn" in the literature.
Hi Dave
No this is not correct.
The OSWG stems from an attempt to solve for the wavefront in a horn. It is not possible to do this with Webster's equation. The OSWG was simply one of the exact solutions that I found that had the requirements for a throat wavefront that I was looking for (flat circular wavefront). Others require square apertures or curved wavefronts - as is the case for a conical waveguide - which existing compression drivers do not supply (although they could. I have several patents on this aspect of the problem.)
Hence, initially I did not see that the OSWG would be ideal, but it did turn out to be, as I have shown AND the guy in Australia has shown. Constant directivity requires a constant velocity across the curved wavefront in the mouth. This is not easy to achieve and only a few shapes can do it. The OSWG is one of them. In any device there will always be one mode which has this shape, so all devices do this to a certain extent. But the OSWG does this where the main mode, the uniform one, is the largest with the HOMs being the least. This later fact was simply something that I discovered along the way and not a design intent.
A conical horn, as you suggest, would work exactly like an OSWG if and only if the wavefront in the throat where spherical (but compression drivers are not). Otherwise there will be a multiplicity of HOMs generated and a less than satisfactory result.
My waveguides do not "surpass" the Keele designs in directivity control, I never claimed that, but they do this without the use of diffraction and internal reflection for a smoother far field response. As I have always said, diffraction is great for directivity control, but bad for frequency response. Doing both well was the challenge.
"Any horn with a varying expansion rate and a continuosly flaring wall contour will have higher directivity at high frequencies" This is widely believed, but incorrect. There is no mathematical reason that this should be so. A radial piston in a sphere does NOT have a collapsing directivity, this is well known (see Morse). So it IS possible. It does become ever harder to do because all compression drivers have non-flat wavefronts at HFs and this can cause a collapsing directivity.
When I first had this idea I built a waveguide in an actual sphere which was driven by a honeycomb flat piston. It did not have a narrowing HF response. I believe that these results were published in JAES.
Basically what you are saying is the old concept of how horns work. I have had these discussions with Don Keele many times before. He acknowledges the data (which shows that the directivity does not narrow) but isn't clear on why that happens. I ask him the same thing that I'll ask you. Why should it? What math shows that it will? There isn't any.
Last edited:
Earl,
Here is just one example that can be found in the literature. There are many others if you do the correct Google search. I wouldn't put much value in what a Wiki says, that is not ever a great source of information.
Patent US4486725 - Protective sheath for a waveguide suspended ...
www.google.com/patents/US4486725
The sheathing permits the waveguide array to assume and retain catenary configuration under varying loads minimizing inflections and detrimental local ...
Here is just one example that can be found in the literature. There are many others if you do the correct Google search. I wouldn't put much value in what a Wiki says, that is not ever a great source of information.
Patent US4486725 - Protective sheath for a waveguide suspended ...
www.google.com/patents/US4486725
The sheathing permits the waveguide array to assume and retain catenary configuration under varying loads minimizing inflections and detrimental local ...
I'm a fan of the 2360A horn.
We install a regular number of 4675 cinema systems that are based around it. They are easy to EQ and give great uniformity across the audience area. I've also heard it set up in a large scale domestic setting and it sounds good with careful EQ of the usual CD fall off (which is really a compression driver fall off). Except for getting a little messy above 10kHz the response is very good at all angles.
They can go very low in frequency although I have noticed that there is variation from one compression driver to the next in terms of sounding pure below 1kHz.
My suspician is that JBL wants to discontinue this one as their new series is considerably cheaper to build.
David
This is not correct. OSWG are NOT specific values of a set of hyperbolic curves. They are completely different functions. This is fundamental.
I do not know the non-acoustic literature. Can you find one that is acoustic related?
Earl,
I wasn't saying that the oblate spheroid was an exponential, just that there is more than one end result while using that equation depending on the choice of exponent value. I was saying that in a catenoid you can also vary the values and get a different result. An oblate spheroid describes the Earths shape but that does not mean there is only one exact shape of that type of Sphere. That medical device and other ultrasonic waveguides are still waveguides though not for audio frequencies that we are working with here. The shape is also used in Sonar so you can say these are not audio, but in reality they are just used in a different frequency range than for human hearing. Let's end this now, I am not arguing with you, Yours was the first instance of that term. oblate spheroid used in audio that I know of. That is your application and addition to the audio waveguide design field.
I wasn't saying that the oblate spheroid was an exponential, just that there is more than one end result while using that equation depending on the choice of exponent value. I was saying that in a catenoid you can also vary the values and get a different result. An oblate spheroid describes the Earths shape but that does not mean there is only one exact shape of that type of Sphere. That medical device and other ultrasonic waveguides are still waveguides though not for audio frequencies that we are working with here. The shape is also used in Sonar so you can say these are not audio, but in reality they are just used in a different frequency range than for human hearing. Let's end this now, I am not arguing with you, Yours was the first instance of that term. oblate spheroid used in audio that I know of. That is your application and addition to the audio waveguide design field.
The departure angle in the 2360 (that is, the angle of the "cheeks" relative to the diffraction slot) seems milder in the 2360 than in the 2344- is that the case? I'd think this would help mitigate the harshness from the diffraction slot. When I heard 4430s, I noticed some glare/harshness, particularly at high levels, though I don't know if that's from trying to get 20k out of the titanium 2425h, or from the slot. I'm assuming a bit of both.
The current array horn is pretty much just a variant on the same theme, though it does away with the scale of the "cheeks" and the angle is fairly shallow. Why they don't bother to terminate it properly in the horizontal (the arrays use the horn rotated 90 degrees from typical 90x40 horn installs) is beyond me.
To be clear, I certainly do not minimize the importance of Geddes' contribution by saying the catenoid was defined as a Salmon shape. I was actually implying I thought it was a long forgotten shape he rediscovered, using it in a different configuration for an even more significant role.
Of course there are an infinite number of catenoids. There are an infinite number of exponentials and hyperbolics too. An infinite number of every curve like that.
And the Webster equation is an approximation, I think we would all agree. Some horns modeled with the formula are pretty close to what it defines, others don't fit the model as well. None are exact except maybe a straight pipe driven with a plane wave.
My point is that the catenoidal horn was described by Salmon. In order to be reasonably closely approximated by Webster's equation, it would have to be long and narrow, but still, the catenoid was defined as a specific case of Salmon family horn. That was interesting to me. When the mouth is opened wide, Webster's equation does becomes less accurate, but it does for all kinds of other shapes too.
A catenoidal horn that's long and narrow can be used as a basshorn, one that provides strong acoustic loading. Another catenoid that's short and wide can be used as an HF waveguide, giving less acoustic loading but a wider pattern. In a way, those statements are almost self-evident, but it does show a pattern. There is a continuum of catenoidal horns, and many are potentially useful. To me, that's fairly significant.
There are a lot of interesting papers out there to study, some that I think are very useful. The fact that the catenoidal horn was described by Salmon means that there is a lot of work that applies, at least to some forms of the catenoid. Add the work done to improve and/or change the model to allow for wavefront curvature, and there's even more useful information to draw upon. I think there is a lot of relevant research that applies to this subject, some old, some new.
Of course there are an infinite number of catenoids. There are an infinite number of exponentials and hyperbolics too. An infinite number of every curve like that.
And the Webster equation is an approximation, I think we would all agree. Some horns modeled with the formula are pretty close to what it defines, others don't fit the model as well. None are exact except maybe a straight pipe driven with a plane wave.
My point is that the catenoidal horn was described by Salmon. In order to be reasonably closely approximated by Webster's equation, it would have to be long and narrow, but still, the catenoid was defined as a specific case of Salmon family horn. That was interesting to me. When the mouth is opened wide, Webster's equation does becomes less accurate, but it does for all kinds of other shapes too.
A catenoidal horn that's long and narrow can be used as a basshorn, one that provides strong acoustic loading. Another catenoid that's short and wide can be used as an HF waveguide, giving less acoustic loading but a wider pattern. In a way, those statements are almost self-evident, but it does show a pattern. There is a continuum of catenoidal horns, and many are potentially useful. To me, that's fairly significant.
There are a lot of interesting papers out there to study, some that I think are very useful. The fact that the catenoidal horn was described by Salmon means that there is a lot of work that applies, at least to some forms of the catenoid. Add the work done to improve and/or change the model to allow for wavefront curvature, and there's even more useful information to draw upon. I think there is a lot of relevant research that applies to this subject, some old, some new.
You did, actually: "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.... " That sounds like a claim that your's surpass all others.
We both agree that horn design is about the art of compromise amongst a number of factors.
I know it is the old thinking, I just didn't realize it was wrong thinking. With regard to high frequencies beaming within horns, this is simply diffraction theory and how waves of a given wavelength bend around an object of a given size. I hope that isn't an obsolete theory!
David
Diffraction theory applied as you are trying to do is wrong. There does not have to be "high frequencies beaming within horns" so if your "diffraction theory" implies that there is then it is wrongly applied.
Thank you for recognizing that. Even in my first paper I acknowledged the Freehafer solution (which is not A Salmon horn), so I know that the contour was know. But I don't think that anyone had recognized its significance. It sounded like you guys were saying that it was.
Last edited:
- Status
- Not open for further replies.