= Far-field acoustic force and stress moments
{title2=$\rho'=\frac{n_in_j\ddot S_{ij}}{4\pi c_0^4r}+\frac{n_i\dot F_i}{4\pi c_0^3r}$}
For compact <Lighthill stress tensor> and applied-force distributions, define $S_{ij}=\int T_{ij}\,d^3y$ and $F_i=\int f_i\,d^3y$. Differentiating the <retarded acoustic Green function> at far distance gives the displayed leading radiation field, evaluated at $t-r/c_0$. Source compactness requires its size to be small compared with the acoustic wavelength, not merely with the observer distance.
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