Posted by Wayne Parham [ 65.69.120.122 ] on January 07, 2004 at 06:32:06:
In Reply to: In the Corner Horns? posted by Garlando on January 06, 2004 at 16:53:36:
A cornerhorn is loaded from the apex of the floor/wall corner junction, but at very low frequencies (below 35Hz for 8 foot ceilings), the ceiling becomes a loading boundary too. Above 35Hz, the apex expansion is eighth-space but below 35Hz is it greater than eighth-space. There's actually a sort of transition region between 35Hz and 70Hz where it is increasing above eighth-space, so for most of the bass region, it is greater than eighth-space and steadily increasing as frequency drops.
Another way to look at it is that the corner forms a three-sided pyramid-shaped conical horn having an expansion equivalent to a four-sided horn with 70o wall angles. It's sort of like a giant 70o CD horn. But below 35Hz, the wavelength is long enough that the entire height of the wall/corner junction comes into play, not just the expansion from the floor apex. At very low frequencies the launch corner isn't a three-sided pyramid but rather it is a four sided boundary having horizontal flare of 90o and parallel vertical sides. This is a different spatial orientation than the corner apex triangular pyramid, and has a different expansion rate. It acts like a tightly constrained space with increasing directivity as frequency drops.
To illustrate, see the following charts:
Distance from apex 1 2 3 4 5 6 7 8
Cross-section area 2 8 18 32 50 72 98 128
Equivalent rectangular 70.53o 70.53o 70.53o 70.53o 70.53o 70.53o 70.53o 70.53o
horn flare angle
Compare the chart above with a rectangular horn having straight walls and 70.53o flare:
Rectangular pyramid-shaped horn with straight walls and 70.53o flare
Distance from apex 1 2 3 4 5 6 7 8
Cross-section area 2 8 18 32 50 72 98 128
From this, we see that the expansion of a room corner has area expansion equal to that of a rectangular horn having 70o flare. But now lets look at the expansion of the corners, when the cross-section includes the floor and ceiling, and is made as vertical sections.
Distance from corner 1 2 3 4 5 6 7 8
Cross-section area 16 32 48 64 80 96 112 128
Equivalent pyramidal 127o 109o 98o 90o 84o 78o 74o 70o
horn flare angle
The equivalent expansion is very wide for the first eight feet, but above 100Hz or so, this is not relevant. For wavelengths shorter than 8 feet, the ceiling is a reflector and not a source launch boundary. For wavelengths longer than 8 feet (about 140Hz), the ceiling begins to act more and more as part of the source boundary, and a constrained space greater than eighth-space. It acts more like a horn having narrowing directivity as frequency goes down.
So lets see what happens beyond 8 feet:
Distance from corner 9 10 11 12 13 14 15 16
Cross-section area 144 160 176 192 208 224 240 256
Equivalent pyramidal 67o 65o 62o 60o 58o 56o 55o 53o
horn flare angle
As you can see, area expansion narrows further out from the corner. It forms an expansion characteristic that is similar to a parabola, when the expansion is carried out past 8 feet. So the corner could be seen as a horn having conical expansion for the first 8 feet, and then a parabolic expansion after that. It could also be viewed as eighth-space for the first 8 feet, and then increasingly greater than eighth-space beyond that.
The depth of the room to opposing walls make standing waves, and so there are other issues at play here. Height from the floor is also important - One might want to crossover to MF/HF horns having controlled dispersion so that "floor bounce" reflections don't cause deep nulls. And all room modes are excited pretty much evenly from a cornerhorn, so there is that to consider. But even if the room were very large so that room modes were shifted down under the audio bandwidth, you would still have the spatial conditions described above, and the energy concentration resulting from it.
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