As a matter of historical record, Dr. Geddes, when did you first publish an article about the OSWG horn? Or was the first reference in your book (which I remember buying at the RMAF a few years ago)?
I think it's significant because a low-diffraction horn is an important milestone in the history in audio, and you were the first there. Newell and Holland refer to a proprietary low-diffraction horn in their book, but they say little about how it was designed.
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My first paper was at the 91st AES convention back in 1991.
I was presented to the concept in an earlier AES paper on modeling horn drivers. I realized in that paper that the exponential horn, which was used in the device that was measured to test the model, could not be used for predicting polar response. Having a model of horns that could not predict polar responses was kind of pointless. So I looked for another method. When I found the OS coordinates in Skudryk I realized that they would have exact solutions to devices that looked very much like real horns.
I was presented to the concept in an earlier AES paper on modeling horn drivers. I realized in that paper that the exponential horn, which was used in the device that was measured to test the model, could not be used for predicting polar response. Having a model of horns that could not predict polar responses was kind of pointless. So I looked for another method. When I found the OS coordinates in Skudryk I realized that they would have exact solutions to devices that looked very much like real horns.
Some Horn History
The hyperbolic horn (A.K.A. O.S. Waveguide) is not new in the field of acoustics.
While At M.I.T.,
[1] John Freehafer submitted his PHD dissertation,
“The Velocity Potential of a Hyperbolic Horn”
On 13-May-1937
https://dspace.mit.edu/bitstream/handle/1721.1/46001/35368752.pdf?sequence=1
Shortly thereafter,
[2] Vincent Salmon submitted his PHD dissertation
“The Sound Field and Radiation Impedance of a Hyperbolic Horn”
on 6-Dec-1938
http://dspace.mit.edu/bitstream/handle/1721.1/45994/35167649.pdf?sequence=1
Regards,
WHG
The hyperbolic horn (A.K.A. O.S. Waveguide) is not new in the field of acoustics.
While At M.I.T.,
[1] John Freehafer submitted his PHD dissertation,
“The Velocity Potential of a Hyperbolic Horn”
On 13-May-1937
https://dspace.mit.edu/bitstream/handle/1721.1/46001/35368752.pdf?sequence=1
Shortly thereafter,
[2] Vincent Salmon submitted his PHD dissertation
“The Sound Field and Radiation Impedance of a Hyperbolic Horn”
on 6-Dec-1938
http://dspace.mit.edu/bitstream/handle/1721.1/45994/35167649.pdf?sequence=1
Regards,
WHG
Hi whgeiger,
Thank You for the data You have give us.
Very interesting.
Reagrds
Ivica
Eugen Skudrzyk [3]
For the wave equation expressed in spheroidal coordinates see Chapter 22 of
[3] The Foundations of Acoustics: Basic Mathematics and Basic Acoustics
http://dls.bookzz.org/genesis/969000/8b4eec7b7d3589660ff0cef6d8999c6b/_as/[Eugen_Skudrzyk__(auth.)]_The_Foundations_of_Acous(BookZZ.org).pdf
Regards,
WHG
For the wave equation expressed in spheroidal coordinates see Chapter 22 of
[3] The Foundations of Acoustics: Basic Mathematics and Basic Acoustics
http://dls.bookzz.org/genesis/969000/8b4eec7b7d3589660ff0cef6d8999c6b/_as/[Eugen_Skudrzyk__(auth.)]_The_Foundations_of_Acous(BookZZ.org).pdf
Regards,
WHG
hi whgeiger,
thank You for the book.
yes I have seen chapt.22
trying to see if there is any other horn flare function that would have lower 2nd derivate.
It seems that some combination can give promissing results, I have no idea what would be the criteria in the curve comparison.
regards
ivica
Link works!
That is a problem at your end. The link works when I click on it. Send me a private message with your e-nail address. The file size is 60 mb.
That is a problem at your end. The link works when I click on it. Send me a private message with your e-nail address. The file size is 60 mb.
Code:
This link works:
http://dls.bookzz.org/genesis/969000...6d8999c6b/_as/
This non-auto-hyperlinked link doesn't
http://dls.bookzz.org/genesis/969000...6d8999c6b/_as/[Eugen_Skudrzyk__(auth.)]_The_Foundations_of_Acous(BookZZ.org).pdfOuch! 🙁 My copy of Skudrzyk cost me something like $120 and that was back in the 80's. Although mine is signed 🙂
Thanks, I figured it out.
Quite interesting, this means if we use a direct radiating driver, the diaphragm shape must be a spheroidal shell that matches the coordinate? So it could be flat, concave, or convex? But the motion of real drivers would be quite different from the vibrating spheroidal shell if I understand it correctly. In such case we need to provide a differently shaped throat wave front.
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Nuts & Bolts
What it means is that you should not use a direct radiating driver in a horn.
You cannot 'sculpt' a wave front with a driver alone, a phase plug is needed to fill this mission as well as others.
The reasons for this are numerous. I will give just a few here:
1) Typical driver diaphragms are not flat for one good reason: that geometry does not yield the stiffest structure for a given (minimal) mass of material.
2) A curved diaphragm made from a solid material that grows and shrinks in size at sound frequencies to produce wave fronts that match its shape, is not physically realizable given present technology.
3) If you place the driver diaphragm at the apex of the horn, then a flat disk piston meets the ideal requirement. Note however, that the upper frequency bound is set by the piston radius [r]. While a larger [r] provides more output [Vd] for a given displacement [Xmax], the larger [r] is, the lower the frequency for the onset beaming as well as piston breakup modes and horn HOM's. Note that these facts also apply to non-flat diaphragms as well.
This is why a phase plug is interposed between a much larger diaphragm and a much smaller horn throat. Its presence is mandatory and its mission is fairly well defined as implied here.
As the nut said to the bolt: "not without a washer baby!"
Regards,
WHG
What it means is that you should not use a direct radiating driver in a horn.
You cannot 'sculpt' a wave front with a driver alone, a phase plug is needed to fill this mission as well as others.
The reasons for this are numerous. I will give just a few here:
1) Typical driver diaphragms are not flat for one good reason: that geometry does not yield the stiffest structure for a given (minimal) mass of material.
2) A curved diaphragm made from a solid material that grows and shrinks in size at sound frequencies to produce wave fronts that match its shape, is not physically realizable given present technology.
3) If you place the driver diaphragm at the apex of the horn, then a flat disk piston meets the ideal requirement. Note however, that the upper frequency bound is set by the piston radius [r]. While a larger [r] provides more output [Vd] for a given displacement [Xmax], the larger [r] is, the lower the frequency for the onset beaming as well as piston breakup modes and horn HOM's. Note that these facts also apply to non-flat diaphragms as well.
This is why a phase plug is interposed between a much larger diaphragm and a much smaller horn throat. Its presence is mandatory and its mission is fairly well defined as implied here.
As the nut said to the bolt: "not without a washer baby!"
Regards,
WHG
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Having tried different dust cap shapes on a wide range driver, and performed Klippel scans on them, I think I have a reasonable feel how to shape it to provide a more wider pattern while having optimum stiffness. Just haven't tried the concept in a horn using a tweeter using such shapes.
Hi Gedlee,
Finally, I have tried several curves (near the throat) and if the the integral of the 2nd derivative is the "measure of the goodness" (less is better) then OSWG curve (the integral its 2nd derivative) would be the best. I have tried OSWG, QT-WG, COSH, hyperbolic,...for the desired angle of 45 degs. Horn length about 20cm. Almost all of them have reached desired angle after about 4 to 5 cm from the throat.Initial throat radius is 2.5cm. and throat initial wall angle is set to be 0 deg.
Interestingly, QT-WG curve is almost as COSH curve with Fo=1450Hz. So I believe that from such frequency most of the horn can be used.
If the desired angle is set to 30 deg, that (Fo) frequency is about 850Hz.
Is there any more info about OSWG horn throat impedance data depending on the horn wall angle?
Regards
Ivica
This isn't true as my products show. Just look at the HF response and you will see that it is not changing. There is no limit from the piston radius. Piston "beaming" is a phenomena that occurs in a flat baffle. That is not the case here. It would become true IF the angle of the waveguide went to 180 degrees, but then that's not really a waveguide.
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My papers and book have as much information as you are likely to find. Basically, for a fixed throat radius, as the angle is increased the peak in the impedance - after its initial rise - moves higher in frequency. You might tend to call this "cut-off" except that it isn't that sharp. It is more like a high-pass filter with a Q of 1->2.
Hi Gedlee,
yes I have realized that, with constant throat radius (as an example I have started with 1-inch radius) increasing the angle impedance peak "moves" towards higher frequency. As I said in previous post the shape of the throat is something like COSH but in order to compare I have changed its Fo (cut-off frequency) until is possible to get that strain ray from the throat center to tangent COSH curve under desired angle -Theta-[ almost the same angle as been in the
OSWG formula y=Ro*sqrt(1 +(x*2*pi*tan(Theta)/(Lamb0))^2) ]
and as said for 1-inch radius (2"driver) and Theta=45 deg, I have get such called 'cut-off" frequency about 1450Hz. I believe that for the OSWG the almost the same result can be expected, but it would be nice if You can suggest more exact formula or table, for 1", 1.5" and 2" drivers type.
Angle, may be 30 deg, and 45 deg (Off-axis)
Regards
Ivica
Tail Gunner Joe
You hijacked my statement out of its context where [r] is materially represents both the horn throat radius and driver diaphragm radius as well.
Like many others, your products use compression drivers and horns with small [r] <= 1" for the horn throat and the effective piston radius that appears at the phase plug exit as well.
So what is the purpose of the fallacious claim you make here?
WHG
You hijacked my statement out of its context where [r] is materially represents both the horn throat radius and driver diaphragm radius as well.
Like many others, your products use compression drivers and horns with small [r] <= 1" for the horn throat and the effective piston radius that appears at the phase plug exit as well.
So what is the purpose of the fallacious claim you make here?
WHG
I show a couple of examples in my book and papers, but for all those combinations you would have to go through the math yourself. There is no simple formula.