Acoustic horns convert large pressure variations with a small displacement area into a low pressure variation with a large displacement area and vice versa. It does this through the gradual, often exponential increase of the cross sectional area of the horn. The small cross-sectional area of the throat restricts the passage of air thus presenting a high impedance to the driver. This allows the driver to develop a high pressure for a given displacement. Therefore the sound waves at the throat are of high pressure and low displacement. The tapered shape of the horn allows the sound waves to gradually decompress and increase in displacement until they reach the mouth where they are of a low pressure but large displacement.

A modern electrically driven horn loudspeaker works the same way, replacing the mechanically excited diaphragm with a dynamic or piezoelectric loudspeaker.

Modern horn designs typically feature some form of conical, exponential or tractrix taper. Roughly speaking, the slower the flare rate, the deeper and lower frequencies the horn will reproduce for a given length of horn. For example, a horn area growth rate of 30% per foot will allow reproduction down to about 30 Hz; 10 times area per foot provides midrange reproduction; 100 times area per foot is used in high frequency horns.

Modern high output horns also make the throat area of the horn smaller than the cone diaphragm area. This is called the “loading” or “compression” ratio of the horn. The compression ratio is the cone area divided by the throat area. Typically for bass and midrange frequency the compression ratio is from (1.5 to 1) low compression to normal compression (2 to 1) to high compression (3.5 to 1). High frequency compression drivers sometimes have compression ratios as high as 10 to 1.

The higher the compression the greater the horn’s ability to properly couple the diaphragm to the air at the horn’s mouth, increasing efficiency, until the compression ratio is so high that it actually begins to impede cone motion. At this point the maximum sound output power from the horn (at a given distortion) will be reduced. To demonstrate this at an extreme, place a cone woofer face down on a concrete floor. The compression ratio will be very high, however sound output from the back of the speaker will be quite low.

http://en.wikipedia.org/wiki/Horn_loudspeaker