= Rayleigh integral for baffled acoustic radiation
{c}
{title2=$p=-\frac{\rho\omega^2}{2\pi}\int f(x')e^{i\omega(t-R/c)}R^{-1}\,dS'$}
= Rayleigh aperture integral
{c}
{synonym}
An aperture in a rigid plane with prescribed harmonic normal displacement $f(x')e^{i\omega t}$ radiates into a half-space. Superposing <acoustic monopoles>, each doubled by its same-sign rigid-wall image, gives the stated integral, where $R$ is the distance from aperture element to observer. In the <acoustic far field>, expanding $R$ to first order across the aperture identifies the angular radiation amplitude with the aperture's <Fourier transform>.
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