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Old 4th December 2013, 08:18 PM   #6691
gedlee is offline gedlee  United States
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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.
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Old 4th December 2013, 08:42 PM   #6692
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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.
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Old 4th December 2013, 09:27 PM   #6693
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Originally Posted by gedlee View Post
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?!
I doubt that many here were confused at all about it, but what fun is that? (:
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Old 4th December 2013, 10:19 PM   #6694
gedlee is offline gedlee  United States
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Originally Posted by Kindhornman View Post
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.
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Old 2nd May 2014, 10:33 AM   #6695
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Wow, long time no chat here!

I am using mabat's equation to calculate an OS profile, but now I would like to also calculate the area expansion (with the correct wavefront shape).

Any clue?
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Old 2nd May 2014, 02:58 PM   #6696
JoshK is offline JoshK  Canada
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Wow, long time no chat here!

I am using mabat's equation to calculate an OS profile, but now I would like to also calculate the area expansion (with the correct wavefront shape).

Any clue?
My best guess is to go to where the math came from. Oblate spheroidal coordinate transforms that allow nice solutions to PDEs. The transform should relate the waveform shape and expansion.
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Old 2nd May 2014, 03:05 PM   #6697
gedlee is offline gedlee  United States
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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?
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Old 3rd May 2014, 07:58 PM   #6698
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Default 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
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Old 3rd May 2014, 10:11 PM   #6699
gedlee is offline gedlee  United States
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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.
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Old 3rd May 2014, 10:57 PM   #6700
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Quote:
Originally Posted by gedlee View Post
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.
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.

Last edited by whgeiger; 3rd May 2014 at 11:05 PM.
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