= Acoustic thickness noise
{title2=$\partial_t(\rho_0v_n\delta_s)$}
Thickness noise is the sound generated by displacement of fluid by a moving impermeable body, represented by the surface <acoustic monopole> term. For a <rigid body>, $\int_Sv_n\,dS=d\mathcal V/dt=0$, so its leading <acoustic compact-source approximation> has no net-volume monopole. Its local source need not vanish: a moving finite-volume body can radiate through higher spatial moments. A thin-body or negligible-volume approximation is needed when all such radiation is to be omitted.
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