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

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12.7. Radiation from a rectangular cap in a sphere

A useful model for the mouth of a circular horn is the spherical cap in a sphere [3]. However, this can be shown to have a somewhat irregular on-axis response with peaks and dips due to interference between sound radiated from the center of the cap and its perimeter. In addition, circular horns are rarely used these days, and it is more common to find a rectangular horn with an aspect ratio chosen so that its horizontal radiation is concentrated over an angle which covers the auditorium area. However, one additional advantage of this arrangement is that on-axis irregularities are less likely. The question we wish to answer is what is the optimum aspect ratio for a smooth on-axis response? Until ...

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