This is slightly off-topic, and it is also a bit of hair-splitting. But it is significant enough to mention, an easy-to-miss factoid. The only reason I even notice the distinction is one of my flagship products is a constant directivity cornerhorn, which makes use of the trihedral expansion of the corner to form what is essentially a very large waveguide. So I've analyzed this configuration a great deal over the last 30 years or so.
The exapansion formed by a trihedral corner (eight-space boundaries) is not the same as a square 90° conical horn. The area expansion is closer to what a 70° square horn would make. The horizontal angle is 90°, to be sure, and that's the most important feature. But the fact that the trihedral corner's expansing cross-section is different than an expansing rectangular cross-section makes its DI slightly different. And of course, this makes the simplifying assumption that the trihedral boundaries are the only ones present, which is rarely the case. Usually "eighth-space" is what people consider a room's corner to be, but of course, it isn't. The expansion from the room's corner is only somewhat "conical" until it reaches the ceiling, in which case it begins to become more of a parabolic expansion. Then by the time expansion reaches the opposite wall, it closes up completely. So indoors spaces are always constrained more than the major fractional radiating spaces we commonly talk about, i.e. halfspace, quarter-space, and eighth-space.
Good point Wayne, after reading Buckminister Fuller should have recognized a square corner as a trihedra
.All the 90s in my post 20 should be revised to 70s.
Art
Hi Wayne,
The area expansion rate of a corner is the same as that of a triangular 90° conical horn. It is also the same as that of an axisymmetric (circular cross-section) conical horn having an included angle of 82.8°.
Kind regards,
David
David,
Using a conical horn having an included angle of 82.8° (and let's say one meter depth), does the high frequency response simulation change in Hornresp going from 1/8 space to whole space?
Does the simulation assume isophase wavefronts?
Art
That depends on the size of the horn. If the horn is acoustically small, then corner loading acts as an extension of sorts. It smooths the response ripple. But if the horn is acoustically large already, the boundaries have no effect. Hornresp has shown this kind of detail since its earliest versions.
If the horn angle matches the wall angle of the corner, the boundaries actually become the horn provided it is placed near enough to the apex. So there is no directivity change, except for the improved pattern control down low.
If the horn angle matches the wall angle of the corner, the boundaries actually become the horn provided it is placed near enough to the apex. So there is no directivity change, except for the improved pattern control down low.
We seem to be in complete agreement, but when I did some checks in Hornresp they did not “show this kind of detail since its earliest versions”.
Perhaps you could post some Hornresp charts that show the HF response not changing from from 1/8 space to whole space, with the parameter screen, I don’t seem to be able to duplicate what you and I agree should happen.
I don't have screen shots of stuff I did a dozen years ago, but I do remember modeling these conditions very early on in the Hornresp life cycle. I don't know what the first versions were, whether I used version 1 or 2, but I do know that I used version 3.1. That sticks in my mind because of the popular Windows product of the early nineties with the same version number.
Even back then, you could model a truncated conical horn in freespace and see the response ripple, but then put it in eighth-space and see the response become smoother. You could model a large conical horn with the same area expansion as a trihedral corner radiating into freespace and it would provide the same response as a truncated horn in eighth space. So these two conditions provided the same simulated results, as they should have.
Even back then, you could model a truncated conical horn in freespace and see the response ripple, but then put it in eighth-space and see the response become smoother. You could model a large conical horn with the same area expansion as a trihedral corner radiating into freespace and it would provide the same response as a truncated horn in eighth space. So these two conditions provided the same simulated results, as they should have.
Hi Art,
Hornresp cannot simulate a conical horn having an included angle of 82.8° and an axial length of 1 metre - the mouth area is greater than the allowable upper limit of 99999.99 sq cm. As far as the high frequency response changing on switching from 1/8 space to whole space is concerned, it depends on whether power response or pressure response is being considered.
Hornresp automatically selects the most appropriate wavefront model for the horn being simulated. A tractrix horn for example, would use the isophase wavefront model. A low flaring rate exponential tapped horn with a relatively small mouth would use the plane wavefront model.
Kind regards,
David
Hornresp cannot simulate a conical horn having an included angle of 82.8° and an axial length of 1 metre - the mouth area is greater than the allowable upper limit of 99999.99 sq cm. As far as the high frequency response changing on switching from 1/8 space to whole space is concerned, it depends on whether power response or pressure response is being considered.
Hornresp automatically selects the most appropriate wavefront model for the horn being simulated. A tractrix horn for example, would use the isophase wavefront model. A low flaring rate exponential tapped horn with a relatively small mouth would use the plane wavefront model.
Kind regards,
David
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