Essentially, for lack of wnating to wtie a 15 page description on it, a horn takes advantage of reflections, and standing waves, since standing waves, unless out of phase aren't of poor quality, just out of proportion, so in a harn, a tone is reflected over and over upon itself amplifying the wave, but when the horn terminates, it continues like any other wave, and stops reflecting, unless it reflects from a surface in the room. So your amplified wave, in the acoustic environment, acts as though the end of the horn were the speaker, not the sub way up in the box.
It is actually much more complex, but that somewhat sums up the principle.
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