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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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9.14. Bends in horns

A horn loudspeaker for use at low frequencies is very large and long, because the flare rate m must be small for a low cutoff frequency and the area of the mouth must be large to radiate sound properly. As a consequence, it has become popular to “fold” the horn so that it will fit conveniently into a cabinet of reasonable size.
Many types of folded horns have been devised that are more or less successful in reproducing music and speech with satisfactory frequency response. To be successful, the bends in folded horns must not be sharp when their lateral dimensions approach a half wavelength, or they will change the spectrum of the radiated sound.
Useful data on the comparative performance of folded horns are not available. ...

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