esp article
I am the person who wrote the waveguide article that appears on the esp website, and have just come across reference to it on page 21 of this thread.
What I would point out to Earl Geddes is that what I said was that the model of a dome tweeter in a conical horn was a reasonable approximation of a point source at the apex of a cone, ( to my knowledge did not at any time attributed this statement to Earl Geddes).
I would submit that this statement is true.
It is true that a dome tweeter is not a pulsating sphere so that its back and forth translations will cause scattering, the point is that if you look at its diameter verses the average excursion it makes the amount of scattering is very small, in fact considerably less than that present when bending a plane wave into a spherical one.
Another point to consider is that a metal dome tweeter has better pistonic action up to high frequencies than a compression driver does, because it is about half the diameter typical of one inch throat compression drivers.
The aberrations visible in the 10kHz. region are due to the vestigial horn and phase plate on the Vifa D25AG tweeter, removing these by and large clears this up.
Overall I can see no reason for using compression drivers in domestic situations unless you have a very large house.
It is true that I did not cite the Geddes book in the article, that is because I haven't read it, and in fact shallow near field horns of the sort I described have little to do with the o.s. type of waveguide as they are not an attempt to find a device that can bend a plane wave into a spherical one with no diffraction, (physicists have known that you can't do this for a very long time, since it is not possible to do this withought scattering and diffraction is proportional to the square of the scattering length).
I would also point out that all of the waveguides I described are in fact straight line and circular arc approximations of a parabola, a curve which has the property of having a constant second derivative, the exact property that gives the o.s. waveguide the minimum diffraction for a given total amount of scattering.
rcw
I am the person who wrote the waveguide article that appears on the esp website, and have just come across reference to it on page 21 of this thread.
What I would point out to Earl Geddes is that what I said was that the model of a dome tweeter in a conical horn was a reasonable approximation of a point source at the apex of a cone, ( to my knowledge did not at any time attributed this statement to Earl Geddes).
I would submit that this statement is true.
It is true that a dome tweeter is not a pulsating sphere so that its back and forth translations will cause scattering, the point is that if you look at its diameter verses the average excursion it makes the amount of scattering is very small, in fact considerably less than that present when bending a plane wave into a spherical one.
Another point to consider is that a metal dome tweeter has better pistonic action up to high frequencies than a compression driver does, because it is about half the diameter typical of one inch throat compression drivers.
The aberrations visible in the 10kHz. region are due to the vestigial horn and phase plate on the Vifa D25AG tweeter, removing these by and large clears this up.
Overall I can see no reason for using compression drivers in domestic situations unless you have a very large house.
It is true that I did not cite the Geddes book in the article, that is because I haven't read it, and in fact shallow near field horns of the sort I described have little to do with the o.s. type of waveguide as they are not an attempt to find a device that can bend a plane wave into a spherical one with no diffraction, (physicists have known that you can't do this for a very long time, since it is not possible to do this withought scattering and diffraction is proportional to the square of the scattering length).
I would also point out that all of the waveguides I described are in fact straight line and circular arc approximations of a parabola, a curve which has the property of having a constant second derivative, the exact property that gives the o.s. waveguide the minimum diffraction for a given total amount of scattering.
rcw
Re: Matching directivity in the vertical and the horizontal planes
I forgot to mention in my last post that the illustrations I provided are based on measurements of real-world horns. In a post I did on AudioRoundTable.com, there are a few additional illustrations that show what happens to the coverage angle when undersized horns are used.
No horn is perfect, and some are better at pattern control than others. Generally speaking, larger horns are better able to control directivity than smaller ones. Of course, using a larger horn requires the acoustic source locations to be further apart too. But if you had a theoretical horn with perfect pattern control having vertical angle smaller than the null angle, then there would be no nulls at all. If there is no energy provided by the tweeter at off-axis angles large enough to cause destructive interference with the woofer, then there is no interference, and therefore, no nulls.
That's not the case in the real world though. Horns do not stop output off-axis, it is simply reduced compared to on-axis. And at some low frequency, they begin to lose directional control. The trick is to balance these trade-offs, and to reduce the vertical angle to approximately that of the null angle. It is also best to use horns with vertical control as low in frequency as possible, ideally down to the crossover frequency. The closer the horn comes to this ideal, the less response anomaly there is in the vertical plane.
I forgot to mention in my last post that the illustrations I provided are based on measurements of real-world horns. In a post I did on AudioRoundTable.com, there are a few additional illustrations that show what happens to the coverage angle when undersized horns are used.
No horn is perfect, and some are better at pattern control than others. Generally speaking, larger horns are better able to control directivity than smaller ones. Of course, using a larger horn requires the acoustic source locations to be further apart too. But if you had a theoretical horn with perfect pattern control having vertical angle smaller than the null angle, then there would be no nulls at all. If there is no energy provided by the tweeter at off-axis angles large enough to cause destructive interference with the woofer, then there is no interference, and therefore, no nulls.
That's not the case in the real world though. Horns do not stop output off-axis, it is simply reduced compared to on-axis. And at some low frequency, they begin to lose directional control. The trick is to balance these trade-offs, and to reduce the vertical angle to approximately that of the null angle. It is also best to use horns with vertical control as low in frequency as possible, ideally down to the crossover frequency. The closer the horn comes to this ideal, the less response anomaly there is in the vertical plane.
gedlee said:
I think the reason for that is that Hoersch was primarily treating the problem of the horn as a receiver (acoustic recording style).
I've seen it referenced a couple of times, all before 1940, IIRC. After Olson published his book, it seems much of the more detailed horn reasearch from the 1920s and 1930s were forgotten, and plane wave approximations became the norm.
Yes, an interesting observation. It seems to correlate quite well with the wave patterns measured by W.M. Hall.
Regards,
Bjørn
Attachments
Earl, I take it that the interior surface of your waveguide is VERY smooth.
Would you be prepared to disclose (or hint at) how you retain the foam plug? (I don't think I've seen any reference)
I'm sitting here with my chamfered 35ppi foam laminations, (ready to join together) and I don't want to use any adhesive that will disturb laminar propagation.
With thanks,
David
Would you be prepared to disclose (or hint at) how you retain the foam plug? (I don't think I've seen any reference)
I'm sitting here with my chamfered 35ppi foam laminations, (ready to join together) and I don't want to use any adhesive that will disturb laminar propagation.
With thanks,
David
Re: esp article
I would still claim that your argument is incorrect. The diameter to excursion ratio is not the issue, its the domes subtended angle that is the issue and the degree to which the diaphragms motion is not normal to the radial angle required by the horn. Excursion has nothing to do with this since the problem exists even if the excursion is zero. The larger the domes subtended angle the greater the error, its that simple. The complete mathematics for this problem is worked out as an appendix to my book and posted on my website. It is probably not readable without my book because it uses technique from other sections of chapter 6 which are not common.
The extent to which this "approximation" causes errors (or how audible they might be) is unclear, principly because I don't use domes, and I don't recommend them. I do not agree that there is "no reason for using compression drivers in domestic situations". I think that there are lots of reasons why a compression driver is the better choice, but these are expounded elsewhere and need not be rekindled here. In a very low cost application I would, and have, used a dome instead of a compression driver, but that was only when cost was a major factor in the design - domes are cheap.
rcw said:
I would still claim that your argument is incorrect. The diameter to excursion ratio is not the issue, its the domes subtended angle that is the issue and the degree to which the diaphragms motion is not normal to the radial angle required by the horn. Excursion has nothing to do with this since the problem exists even if the excursion is zero. The larger the domes subtended angle the greater the error, its that simple. The complete mathematics for this problem is worked out as an appendix to my book and posted on my website. It is probably not readable without my book because it uses technique from other sections of chapter 6 which are not common.
The extent to which this "approximation" causes errors (or how audible they might be) is unclear, principly because I don't use domes, and I don't recommend them. I do not agree that there is "no reason for using compression drivers in domestic situations". I think that there are lots of reasons why a compression driver is the better choice, but these are expounded elsewhere and need not be rekindled here. In a very low cost application I would, and have, used a dome instead of a compression driver, but that was only when cost was a major factor in the design - domes are cheap.
D OB G said:
I use 3M "99" spray adhesive, but only right at the walls of course. You must not block any of the transmission path through the foam. This makes the layered approach difficult to impliment, which is why I don't do it that way. You absolutely must not "glue" the layers together as this glue will seriuosly impeed the sound transmission. Leaving them unattached also has its problems. I just don't see a good method of using "layers".
Re: foam
I have searched wide and far and there are no "good" sources. You either have to buy a "bun" at $1000+, or buy it in rolls and layer it, which, as I have said, does not appeal to me. I used to sell "chunks", but I will need all that I have and the price of that stuff has to be going though the roof. So I'm no longer a source.
angeloitacare said:
I have searched wide and far and there are no "good" sources. You either have to buy a "bun" at $1000+, or buy it in rolls and layer it, which, as I have said, does not appeal to me. I used to sell "chunks", but I will need all that I have and the price of that stuff has to be going though the roof. So I'm no longer a source.
i found a few suppliers :
http://www.mcmaster.com/
http://www.steplaw.com/inventory.html
http://www.foamex.com/technical/filtration.php
http://foamandfoam.com/
which one might be the best one ?
Angelo
http://www.mcmaster.com/
http://www.steplaw.com/inventory.html
http://www.foamex.com/technical/filtration.php
http://foamandfoam.com/
which one might be the best one ?
Angelo
It is true that the velocity profile across the dome surface is an additional source of scattering, but as shown in the KEF, AES paper on dome and waveguide geometry if the dome angle matches the waveguide angle it is a very small effect and has very little effect upon the mouth velocity distribution.
I would also point out that if we take the amount of scattering to be the difference between the actual dome area and the area a wavefront with that velocity profile would have, then the difference between the area of a flat piston and a dome of the same included angle as the horn angle is considerably greater.
What this means is that whatever mechanism we cite, translating the supposedly flat wave at the throat into a spherical wave is in fact a procedure that is liable to produce more higher order modes of greater amplitude.
And in a o.s. waveguide scattering continues to occur at larger diameters leading to lower frequency modes becoming more prominent, and of course the total amount of scattering is much greater.
From these considerations I would conclude that a dome with the correct geometry driving a conical horn with a flared mouth is an inherently better device than a compression driver driving an o.s. waveguide, for the type of sound pressures required for the average domestic sound system.
rcw
I would also point out that if we take the amount of scattering to be the difference between the actual dome area and the area a wavefront with that velocity profile would have, then the difference between the area of a flat piston and a dome of the same included angle as the horn angle is considerably greater.
What this means is that whatever mechanism we cite, translating the supposedly flat wave at the throat into a spherical wave is in fact a procedure that is liable to produce more higher order modes of greater amplitude.
And in a o.s. waveguide scattering continues to occur at larger diameters leading to lower frequency modes becoming more prominent, and of course the total amount of scattering is much greater.
From these considerations I would conclude that a dome with the correct geometry driving a conical horn with a flared mouth is an inherently better device than a compression driver driving an o.s. waveguide, for the type of sound pressures required for the average domestic sound system.
rcw
I totally disagree with your analysis. First, "scattering" is not defined in the context that we are talking about and as a theoretical physicist I don't see how the concept applies.
The HOM proprtion depends only very weakly on the area diference between a flat radiator and a domed one, but very strongly on the dot product of the velocity profile of the radiating surface with the required wavefront shape. You have completely missing this point. Your concepts of "scattering" seem to be getting in the way of your discussion and or understanding. It would be better not to use this term until such time as you can describe it mathematically in the context of this discussion and show mathematically how it realtes. I have done so with the HOM in my AES papers as well as my book, so I'll stick with those well developed concepts.
Your statement "translating the supposedly flat wave at the throat into a spherical wave is in fact a procedure that is liable to produce more higher order modes of greater amplitude." is completely false and all the conclusions that you derive from it are likewise. I can prove that no voice coil driven source can have fewer HOM than a flat throat wavefront compression driver. The deviation of real compression drivers from this flat throat wavefront is indeed an issue, but a much smaller issue than coupling an axial driven dome to a conical horn.
I am not familiar with any KEF papers on this subject. Could you reference that.
The HOM proprtion depends only very weakly on the area diference between a flat radiator and a domed one, but very strongly on the dot product of the velocity profile of the radiating surface with the required wavefront shape. You have completely missing this point. Your concepts of "scattering" seem to be getting in the way of your discussion and or understanding. It would be better not to use this term until such time as you can describe it mathematically in the context of this discussion and show mathematically how it realtes. I have done so with the HOM in my AES papers as well as my book, so I'll stick with those well developed concepts.
Your statement "translating the supposedly flat wave at the throat into a spherical wave is in fact a procedure that is liable to produce more higher order modes of greater amplitude." is completely false and all the conclusions that you derive from it are likewise. I can prove that no voice coil driven source can have fewer HOM than a flat throat wavefront compression driver. The deviation of real compression drivers from this flat throat wavefront is indeed an issue, but a much smaller issue than coupling an axial driven dome to a conical horn.
I am not familiar with any KEF papers on this subject. Could you reference that.
Scattering is very relevant to the issue, I would refer you to Berners paper on piecewise modeling of horns, and also the work of Benade.
The point is that you cannot translate a plane wave into a spherical one withought scattering, you can look at this as there being no mapping of equal length orthogonal trajectories between a plane wave and a spherical one.
It is usual to consider diffraction as being the square of the scattering amplitude, and this leads us to the correct conclusion that if we put all our scattering at one point, say the junction between a cylinder and a cone, that although the total amount of scattering is the same as we might find in an o.s. waveguide, the amount of diffraction is considerably greater in the former case because to minimize diffraction we must ensure that over the interval in which we accomplish our plane to spherical transition, every point must have the same amount of scattering as every other point, thus the need of the relevant wall curve to have a constant second derivative for minimum diffraction becomes immediately obvious.
If you look at mappings between the wavefront produced by a dome piston and a spherical wave however you can clearly see that the set of trajectories is a lot closer to being of the same length as is true of the former case, i.e. there is a lot less scattering, and also potentially a lot less diffraction.
Thus , (as pointed out by Putland), a waveguide for our plane wave is in fact a straight sided tube because we can draw a set of trajectories that are orthogonal and all of the same length, i.e. the wavefronts are parallel and have the same area, this indicates that no scattering has occurred.
If we take a spherical wave in a cone the same thing of course happens, except that the wavefront gets larger in area as it proceeds down the waveguide.
In the case of our plane to spherical translation we are generating spherical waves that unlike plane waves have a complex impedance
that can store energy in the form of standing waves. These manifest in the form of evanescent waves or given the correct combination of frequency and geometry propagate as higher order modes.
Scattering is a more fundamental process than diffraction because it deals with discrete elastic entities, and we model air as being composed of such, when we consider very large assemblages of these particles we can then look at air as an homogeneous medium in which waves can propagate, but sometimes looking at the more fundamental process is a better aid to understanding and i think it true in this case.
rcw
The point is that you cannot translate a plane wave into a spherical one withought scattering, you can look at this as there being no mapping of equal length orthogonal trajectories between a plane wave and a spherical one.
It is usual to consider diffraction as being the square of the scattering amplitude, and this leads us to the correct conclusion that if we put all our scattering at one point, say the junction between a cylinder and a cone, that although the total amount of scattering is the same as we might find in an o.s. waveguide, the amount of diffraction is considerably greater in the former case because to minimize diffraction we must ensure that over the interval in which we accomplish our plane to spherical transition, every point must have the same amount of scattering as every other point, thus the need of the relevant wall curve to have a constant second derivative for minimum diffraction becomes immediately obvious.
If you look at mappings between the wavefront produced by a dome piston and a spherical wave however you can clearly see that the set of trajectories is a lot closer to being of the same length as is true of the former case, i.e. there is a lot less scattering, and also potentially a lot less diffraction.
Thus , (as pointed out by Putland), a waveguide for our plane wave is in fact a straight sided tube because we can draw a set of trajectories that are orthogonal and all of the same length, i.e. the wavefronts are parallel and have the same area, this indicates that no scattering has occurred.
If we take a spherical wave in a cone the same thing of course happens, except that the wavefront gets larger in area as it proceeds down the waveguide.
In the case of our plane to spherical translation we are generating spherical waves that unlike plane waves have a complex impedance
that can store energy in the form of standing waves. These manifest in the form of evanescent waves or given the correct combination of frequency and geometry propagate as higher order modes.
Scattering is a more fundamental process than diffraction because it deals with discrete elastic entities, and we model air as being composed of such, when we consider very large assemblages of these particles we can then look at air as an homogeneous medium in which waves can propagate, but sometimes looking at the more fundamental process is a better aid to understanding and i think it true in this case.
rcw
Angelo, reticulated foam is an open celled foam wherein the cell walls have been removed. You do not want closed cell foam.
The MacMaster Carr parts number I had doesn't work anymore but Patrick Bateman, I'm sure, has it.
I think you might ask Steplaw about distributors in Brazil.
The reticulated foam sold for outdoor furniture upholstery is usually 35 ppi.
Or, you could buy some from Earl.
Air conditioning companies, water filter companies, pond filter companies, marine upholstery companies all carry various grades of polyurethane reticulated foam.
I found some in a foam shop!
The MacMaster Carr parts number I had doesn't work anymore but Patrick Bateman, I'm sure, has it.
I think you might ask Steplaw about distributors in Brazil.
The reticulated foam sold for outdoor furniture upholstery is usually 35 ppi.
Or, you could buy some from Earl.
Air conditioning companies, water filter companies, pond filter companies, marine upholstery companies all carry various grades of polyurethane reticulated foam.
I found some in a foam shop!
angeloitacare said:
Re: foam
I used the 'speaker foam' (bottom of page) from here:
http://www.foambymail.com/Hi-FlowFoam.html
It's only available in 2" sheets so you have to layer it, but for a one-off DIY application it's a reasonable trade-off to make IMHO.
I layered with a *tiny* amount of hot-melt at the periphery of each layer, but MethMan's cotton thread idea occured to me later and I think is worth a try.
angeloitacare said:
I used the 'speaker foam' (bottom of page) from here:
http://www.foambymail.com/Hi-FlowFoam.html
It's only available in 2" sheets so you have to layer it, but for a one-off DIY application it's a reasonable trade-off to make IMHO.
I layered with a *tiny* amount of hot-melt at the periphery of each layer, but MethMan's cotton thread idea occured to me later and I think is worth a try.
rcw said:
I have read, and understood, all the works that you quote and none of them have any relavence to this topic. You are using hand waving arguments and big words (like evanescent) framed with a few irrelavent sources and trying to get me to accept your argument. I don't. I'd like to point out that my entire body of work on this subject has been published and peer reviewed, critiqued and criticized and has held up as completely correct in every case. Your description is however completely new, and as far as I can tell incorrect. Scattering is not a term used in any acoustics text that I know of except as usually defined as the energy "scattered" or diffracted off of an object in space. Internal scattering is not an appropriate terminology and as I said apears nowhere in the literature, and I have read virtually all of it.
Hence, either try and make your arguments using the convention terminology using concrete and defined mathematics or please don't continue to offer these handwaving dissertations as they don't make an impact on me.
To be clear: Either the dome coupled to a cone of the same subtended angle (which to my knowledge doesn't actually exist) or a OS waveguide connected to a plane wave compression driver will have HOMs. As I have said before no "real" source can be made constant directivity with some HOM. Now, of all the surfaces that can connect a circular plane wave to a sperical wavefront, the OS can be proven to genetate the least HOM of any other contour, because it is a catenoid and has a minimum 2nd derivative for a given entry angle. The question then becomes does the dome of equal subtended angle as its conical waveguide (assuming we can find one) have more or less HOM to achieve the same spherical wavefront as that obtained with the OS and the compression driver. That question is unresolved and your arguments don't prove a thing either way.