The idea behind horns (originally) was more to try and achieve the kind of amplification that is possible with an instrument (like a trumpet), where the sound is amplified by the bell shape at the exit. Basically, what happens is the flare causes the air pressure countering the exiting sound pressure waves to match impedance. The result of this matching is something called the transistor effect – where a small input results in an exponentially increased output of the same sound. A great idea, but in practice not easy to achieve 😉