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

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13.15. The far-field pressure distribution as a spatial frequency spectrum of the source velocity distribution

Two-dimensional system

In a two-dimensional system with a planar source, the far-field pressure distribution is given by a generalized version of Eq. (13.279), where u ˜ 0 ( x 0 ) image is the source velocity distribution:
p ˜ ( r , θ ) = ρ 0 c k 2 π r e j ( k r π 4 ) u ˜ 0 ( x ) e j k x 0 sin θ d x 0 = j e j ( k r + π 4 ) 2 π k r F ˜ ( k x ) ,
(13.286)
where
F ˜ ( k x ) =

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