Thanks to Bert Doppenberg, Dr. Bruce Edgar, MARVIN, and others.
This is a collation of information from the internet and personal research. The information may not be accurate (did I really need to tell you that?). Opinions expressed here are my own. The reason for this page is to present my findings on horn speakers. I am not to be held responsible for problems caused by any information or misinformation presented here.
For one answer, see the excellent Thomas Dunker Horn Page and his article Why Horns? For another answer, see Dr. Bruce Edgar's article Why Horns? Basically, horns produce a kind of sound usually unobtainable by direct radiating diaphragms (such as cone or electrostatic speakers). Horns can produce high sound pressure levels (SPLs) with minimal distortion. They tend to be very efficient (or sensitive). Horns sound very dynamic and reproduce fast transients in the music.
Of course, there can be problems associated with horns. They are often hard to build and costly to buy. Poorly designed horns can impart colorations to the music, and sound plain nasty. And horns designed for producing low bass notes must be very large.
Basic Horn Theory
How do horns work? I am not a horn expert and am not qualified to teach you horn theory. However, I will give a summary of horn theory as I understand it. I will provide a lot of references for you to read the theory from qualified experts.
To start with, here is one of the best internet references I have found:
Read this thoroughly to begin to understand horn design and practical use. Also take a look at the Horn References and Resources page.
Horns can be thought of as providing sound reinforcement to a transducer (usually a compression driver). Horns generally have two essential properties: sound directivity enhancement, and acoustic impedance transformation.
A horn provides more sound pressure level (SPL) at a given listening area by increasing the directivity of the sound towards the listener. There is more sound at the listening area, and less sound outside of that area. By analogy, think of focusing a beam of light (from a flashlight or torch). A widely focused beam spreads the light around, reducing the intensity at any one point. However, a narrowly focused beam provides much more light intensity at the center, and much less in the surrounding area.
Consider a point source speaker driver hanging high up in the air. Sound will be radiated off in all directions. Now if we sit the driver on the ground, it has only half the area to radiate into, and acoustic power will be increased by two at any position. If we place the driver at the corner of a floor and a wall, we now radiate into quarter-space, and SPL is increased by four times. Likewise, a driver in a corner will be constrained to one-eighth of the free space area, and SPL is eight times louder.
Each of these increases the directivity. A horn increases the directivity of the compression driver, providing increased SPL in a certain area, over the frequency range for which the horn is designed. The "certain area" is actually a cone with a particular cross-sectional shape and angles describing the spread of the cone away from the driver. Round horns produce round cross sections with a constant angle of spread (for a given frequency). Radial horns have two angular components: a vertical and a horizontal spread. Often the vertical angle is small (compromised) so that the horizontal angle can be large (covering a wider area for an audience in a horizontal plane).
However, round horns and radial horns tend to change their angles of spread (their directivity, measured by the directivity index, or DI) as the frequency changes. This means that high frequencies, for instance, might be more highly directed, and therefore sound louder to someone in a central location than to someone else outside of the center (but still within the horn's low-frequency area of enhancement). To cope with this problem, the constant directivity (CD) horn was invented. The CD horn provides the same SPL at all frequencies within the designed coverage angles.
The second common property of a horn is acoustic impedance transformation. This couples a compression driver to the air. The compression driver has a hard diaphragm, with a very different acoustic impedance to that of air. When we constrict the area/volume of air into which the driver radiates, we increase the acoustic impedance of the air bring it closer to that of the driver. Now, we provide a gradual increase in area until we get to the horn mouth, which is much larger than the throat. The mouth couples the horn throat to the air in the room.
Some compression drivers have very limited travel and power handling, and require this acoustic transformation in order to work at their designed efficiency. However, some modern compression drivers are much more tolerant of power handling. These can often be used in horns that do not focus on providing impedance transformation, such as Constant Directivity horns.