Refraction and diffraction often work hand-in-hand. In lens theory for example, the lens works via refraction up until it becomes diffraction limited. So in this example both things are required for a detailed understanding, but for the most part the diffraction can be ignored and the lens works simply by refraction.
Funny, soon after making my last post looked up refraction, it seemed more appropriate for the primary function of the slant plate lens.
Then looked up the old JBL horn lens brochure, they only mention "lens diffraction effect" in the explanation.
At any rate, they sound warm and fuzzy
.Attachments
At any rate, they sound warm and fuzzy
Which could also be related to a family of mechanical resonances in that assembly, and not entirely acoustic artifacts.
Funny, soon after making my last post looked up refraction, it seemed more appropriate for the primary function of the slant plate lens.
Then looked up the old JBL horn lens brochure, they only mention "lens diffraction effect" in the explanation.
At any rate, they sound warm and fuzzy
I did my MS thesis on slant plate acoustic lenses. They are definitely refraction devices NOT diffraction. But hey, refraction - diffraction, its just a couple of letters. What's the big deal?!
Earl.
Where would refraction come into play in one of those plate lenses on a JBL horn? It seems that you would need a change of medium to have a true refractive change. I don't see how there is anything but diffraction involved here? Can you post that thesis or a link to it, something just doesn't add up for me here.
Where would refraction come into play in one of those plate lenses on a JBL horn? It seems that you would need a change of medium to have a true refractive change. I don't see how there is anything but diffraction involved here? Can you post that thesis or a link to it, something just doesn't add up for me here.
Well I looked at both those articles and from what I see it confirms what I am thinking. I see no change in medium or change in temperature where any refraction would take place. The second article is talking about reflections and not refraction, reflections would appear to be diffraction effects and not refraction effects. Someone want to show me where I am incorrect here?
Yes Earl,
Those horns never worked as described, at least not very well if at all. I do have personal experience with those horns and know them well. This was one of those things that JBL did that just didn't work as planned. The polar response of these horn lenses was pretty bad. Talking about internal reflections back into the horn this takes the cake.
Yes Earl,
Those horns never worked as described, at least not very well if at all. I do have personal experience with those horns and know them well. This was one of those things that JBL did that just didn't work as planned. The polar response of these horn lenses was pretty bad. Talking about internal reflections back into the horn this takes the cake.
First, you need to understand that refraction does not take place within the medium, but at the interface between two different mediums. One medium, in this case, is air and the other the plates. Since the plates require a longer path, the wave speed is slower where they are present. When the slower waves meet up with the airs normal velocity refraction occurs. It is not ideal, which is why it works so bad, but that's the idea.
Got it Earl. At the same time wouldn't the speed in the aluminum plates themselves be faster than the air? It would seem due to the extremely thin aluminum the actual emissivity at the end of the plates would be rather small compared to the air itself except perpendicular to the plate surface area. Refraction would appear to be very minimal while diffraction would seem to be the dominate factor here.
There would be almost no sound going through the metal plates. Even less through the plastic ones. there would be a significant amount of diffraction, yes, which is probably why they didn't work as the theory suggests.
Josh is correct, you would have to do this in the OS coordinate system by integration, just like you would do for spherical coordinates but substituting the definitions from OS. Not an easy task, but not impossible either.
My question would be what do you need the area expansion rate for?
My question would be what do you need the area expansion rate for?
OS Note
Earl, this is for other readers.
To the first degree of approximation, a spherical surface assumption should be sufficiently accurate for calculating the area expansion of horns of circular section, as an OS horn of this variety is asymptotically conical. However, at the horn mouth, wave front geometry gets far more interesting and so does the horn geometry required to mitigate refraction and reflectance of the exiting wave front. Here the horn profile and the wave front as well, necessarily depart radically from the OS régime.
Regards,
WHG
Earl, this is for other readers.
To the first degree of approximation, a spherical surface assumption should be sufficiently accurate for calculating the area expansion of horns of circular section, as an OS horn of this variety is asymptotically conical. However, at the horn mouth, wave front geometry gets far more interesting and so does the horn geometry required to mitigate refraction and reflectance of the exiting wave front. Here the horn profile and the wave front as well, necessarily depart radically from the OS régime.
Regards,
WHG
The mouth is near conical, but the throat is far from that. If one wants the wave front area from the throat to the mouth then it could get complicated. It would be true that this wave front is always a spherical section, but near the throat the radius and angle subtended would vary continuously, starting at an infinite radius and zero subtended angle. Unlike at the throat, near the mouth the radius would vary directly as the distance along the device.
More...
Earl,
The ist. derivative of the horn profile curve (a hyperbola with apex at x=0, y=rt) gives you a tangent line. The intercept of that line with the x axis gives you dx for a given dy. Thus the radius (r) of the approximating spherical cap may be calculated thus: r = ((dx^2)+(dy^2))^(1/2). Of course as r -> oo area of a flat disk is a sufficient approximation.
The area difference between oblate spherical cap having an elliptical profile as opposed to spherical cap having an approximating circular profile is negligible for any circular section OS horn of typical size.
Regards,
Bill
N.B. In my previous post the word refraction should read diffraction. At that time I was thinking about an acoustic lens.
Earl,
The ist. derivative of the horn profile curve (a hyperbola with apex at x=0, y=rt) gives you a tangent line. The intercept of that line with the x axis gives you dx for a given dy. Thus the radius (r) of the approximating spherical cap may be calculated thus: r = ((dx^2)+(dy^2))^(1/2). Of course as r -> oo area of a flat disk is a sufficient approximation.
The area difference between oblate spherical cap having an elliptical profile as opposed to spherical cap having an approximating circular profile is negligible for any circular section OS horn of typical size.
Regards,
Bill
N.B. In my previous post the word refraction should read diffraction. At that time I was thinking about an acoustic lens.
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