Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

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 ) 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 ) = ∫