= Acoustic far field
{title2=$k_0R\gg1$}
The acoustic far field is the radiation region where the observer is many reduced wavelengths from the source and far compared with its geometric extent. Three-dimensional outgoing <acoustic density perturbations> spread as $R^{-1}$; two-dimensional harmonic fields spread as $R^{-1/2}$. The condition is independent of the <acoustic compact-source approximation> $k_0\ell\ll1$. Differentiating a retarded phase produces the radiating part of a <Green function> integral; derivatives of the spreading factor produce near-field terms.
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