In general the amount of diffraction depends on the 2nd derivative of the surface, but there is also a frequency dependence. In actuality diffraction is extremely complex to analyze for arbitrary surfaces so most of what you see and read are heuristic principles. The only detailed source that I know of in acoustics is Foundations of Acoustics by Skudryk.
There is a shadow boundary no matter what the surface radius. Think of light, even a gradual radius throws the same shadow boundary as a sharp radius - this is because the wavelengths are so short. It's just as true in acoustics, except the wavelengths tend to be very long, which causes huge differences in the details of the results.
There is a shadow boundary no matter what the surface radius. Think of light, even a gradual radius throws the same shadow boundary as a sharp radius - this is because the wavelengths are so short. It's just as true in acoustics, except the wavelengths tend to be very long, which causes huge differences in the details of the results.
Hi Gedlee,
That is why I have a hesitation about the OSWG horn wall flare vs JMMLC type,
in my post 7068
http://www.diyaudio.com/forums/multi-way/103872-geddes-waveguides-707.html#post4047379
and Your answer in 7072
as on JMMLC type surface derivation the first, and especially the second derivation of the surface is vary low compared to the OSWG near the horn throat.
Regards
Ivica
ivical - but the JMMLC horns are not constant directivity so you really can't compare them. The OSWG has the lowest 2nd derivative of any device that has a fixed ending wall angle - the shape is a catenoid in this regard. The JMMLC may have a lower 2nd derivative near the throat but to get that same directivity as the OSWG it would have to be greater overall.
I think if you went with a T=0.6 or something close, the directivity is pretty well controlled. But it also depends on the driver as well. I think driver will also influence directivity of an OSWG as well.
Earl, I have a question regarding your loudspeaker construction, a bit OT here but I hope you don't mind...
I read you typically fill your cabinet with the same 30ppi reticulated foam you use in your waveguide (scrap of it actually). Is it completely filled? Nothing else for lining the walls (dense foam, coton, etc.) ?
I understand that the absorption capability of that reticulated foam is only effective in the UHF, so how is it effective inside a woofer enclosure?
I read you typically fill your cabinet with the same 30ppi reticulated foam you use in your waveguide (scrap of it actually). Is it completely filled? Nothing else for lining the walls (dense foam, coton, etc.) ?
I understand that the absorption capability of that reticulated foam is only effective in the UHF, so how is it effective inside a woofer enclosure?
Hi Gedlee,
It is clear to me that if we want constant direcitivity horn we must have a piece of conical horn shape in the larger part of the horn, with faster flare around the horn-mouth in order to suppress mouth reflection on one side and to suppress 'mid-frequency beaming' (D.B.Kelle work) too,
So to use JMMLC shape from throat to the mouth end would not produce CD horn type (for sure). I know, too, that if we want that initial horn wall angle at the throat to be near several degs, using JMMLC curve, the horn would be much longer, as T has to be small, or Lamda0 (horn cut-off Lambda) has to be large-so angular increment would be small, "so many of them have to be done in order to reach the desired angle ".
But I only wonder if some other function ( example parabolic up to reaching desired angle) shape can be used whose 2nd derivative are not so large as OSWG or that can be "controlled in advanced", keeping in mind that the incident wave front has to be parallel (expecting that the sound speed is constant) .
As I have remembered OSWG curve has hyperbola shape as
y=Ro*sqrt{1+ x^2*/[Ro/tg(Q)]^2}
Regards
Ivica
doesn't this argument violate linearity?
acoustic wave propagation at domestic SPL, away from the narrow throat/higher pressure region becomes really close to perfectly linear
I think that I explained that the OS shape is a catenoid in this regard. By that I mean that it is the minimum 2nd derivative connecting the two angles of 0 and the final angle. This is not how I came to this equation, but I later came to realize that it was true and then I did the math, and low and behold it is true. The OS coordinate system - all coordinate systems for that mater - have to obey this rule. It is what they are based on. There is an entire chapter on the Separable Coordinate systems in Morse and Feshbach Methods of Theoretical Physics. (Probably my favorite physics book of all time, along with Morse, Vibration and Sound)
Could we set the beginning and end angles such as 5deg and 90deg to blend with the baffle when trying to find the lowest 2nd derivative curve?
No, no such hyperbola exists. Using OS WG (or any other geometry with CD property), the transition to baffle will allways be of some other shape.
Or do you mean some completely different/arbitrary shape (possibly non-CD), not given by any coordinate system itself?
I would say it all boils down how to terminate the OS profile in the best possible way, reasonable in size...
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Works Both Ways
The change in curvature towards the mouth is linear with propagation distance along the horn bell.
The objective here is to reduce reflectance of the outbound waves.
Note that those that do return are concentrated by the horn in the region where air non-linearity is a concern of yours.
This issue arises due to the necessity to truncate an otherwise infinite hyperbolic horn contour.
The method recommended here provides a smooth transition into a horn bell for the purposes of minimizing reflectance.
This same technique is also used in the design of highway and railway curves, where abrupt changes in direction, presented by a single radius of curvature, are to be avoided as well.
Regards,
WHG
The change in curvature towards the mouth is linear with propagation distance along the horn bell.
The objective here is to reduce reflectance of the outbound waves.
Note that those that do return are concentrated by the horn in the region where air non-linearity is a concern of yours.
This issue arises due to the necessity to truncate an otherwise infinite hyperbolic horn contour.
The method recommended here provides a smooth transition into a horn bell for the purposes of minimizing reflectance.
This same technique is also used in the design of highway and railway curves, where abrupt changes in direction, presented by a single radius of curvature, are to be avoided as well.
Regards,
WHG
It is well known that sound absorption is greater when the material is not placed on a surface. That is because on the surface the velocity must be zero so no absorption occurs there. Logically then the best place to put material in a loudspeaker enclosure is in the middle. This is what I do. It is not completely filled, but more than say 50%. The foam would be reasonably absorptive at frequencies of the enclosures standing waves because the wave passes through it so many times. In the waveguide the primary wave only passes through once.
Thanks for your answer.
Is it better than say basotec (melamine) foam for that task?
What ppi would you choose if you had to use it specifically for that task and that task only?
Why not go for a near 100% fill?
Is it better than say basotec (melamine) foam for that task?
What ppi would you choose if you had to use it specifically for that task and that task only?
Why not go for a near 100% fill?
Pos
I think that it is a good idea to have some sound absorption in the box. But beyond a "reasonable" amount I see no further benefit to it. There is a huge difference between no absorption and what I do, but little difference between what I do and completely filling the box or using some customized material.
I think that it is a good idea to have some sound absorption in the box. But beyond a "reasonable" amount I see no further benefit to it. There is a huge difference between no absorption and what I do, but little difference between what I do and completely filling the box or using some customized material.