There are a lot of other variables though, and the environment that the horn radiates into is certainly one of them. Another is the chamber that precedes the throat. And the back chamber and the electro-mechanical properties of the driver come into play also. But to address your specific comments about the environment, it most certainly does have an impact, and a large one.

Assuming the environment is large, then it can be described by the radiation angle set by the boundaries nearest the sound source. If sound radiates in all directions, like if a speaker is used in wide open space, high above the ground and away from everything, that's called freespace radiation (4π steradians). If the speaker sits on the ground, but there are no other boundaries around, then the radiation angle is cut in half, hence the name half-space (2π steradians). Put a wall behind it, and now this is cut in half again, called quarter-space (π steradians). And if in a corner, it's in eight-space (π/2 steradians).

There are also smaller radiating angles than this, and your very small room may be an example. There is no reason why the radiating angle cannot be made smaller than π/2 steradians. In fact, that is exactly what a horn is - It is a device that reduces the radiating pattern of a sound transducer so that it is made more directional and stronger in the field desired. There are other things in play also, such as compression before the throat and the expansion rate, but one of the main features of the flare is its radiation angle. So in a very real way, the room becomes a part of the horn and it certainly should be considered when designing or implementing a horn system. A basshorn can be made considerably smaller if used in a constrained environment than it would be if used in freespace.

Cheers!
Mike.e

• horn info

To expand on Wayne's statement any room will get both boundary loading (if the speaker is placed close to a wall or corner) and cabin gain, which kicks in at 12dB/octave where the longest room dimension is about a half wavelength. A room with the longest dimension at 12 feet will get cabin gain from about 47 Hz, which means that you don't need to build a horn with an Fc of 20 Hz to get response to 20 Hz; 45 Hz or so will do nicely. When you account for cabin gain and boundary effects in the design process you can make basshorns quite small. With the extreme amount of cabin gain available in a car trunk it actually makes it an ideal place for a relatively small basshorn.

Going to your question, what traditionally limited the use of horns in small rooms was their physical size, not their sound, but today designers like myself are coming up with horns that take advantage of both boundary and cabin gain to create bass horns small enough for even the smallest rooms, including automobile trunks.

Cheers!

The M=0.5-0.6 'optimal' value is applicable for the ideal horns.

On a highly compromised conical segmented horn the differences are less apparent-but on full sized horns it makes a larger difference.

Download the Dinsdale and Edgar horn files from the link below

Cheers!