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
${\tilde{u}}_{0}\left({x}_{0}\right)$
is the source velocity distribution:

$\begin{array}{c}\tilde{p}\left(r,\theta \right)={\rho}_{0}c\sqrt{\frac{k}{2\pi r}}{e}^{-j\left(kr-\frac{\pi}{4}\right)}{\int}_{-\infty}^{\infty}{\tilde{u}}_{0}\left(x\right){e}^{jk{x}_{0}\mathrm{sin}\theta}d{x}_{0}\\ =-j\frac{{e}^{-j\left(kr+\frac{\pi}{4}\right)}}{\sqrt{2\pi kr}}\tilde{F}\left({k}_{x}\right),\end{array}$

(13.286)

where

$\tilde{F}\left({k}_{x}\right)={\int}_{}^{}$

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