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The Ffowcs Williams-Hawkings equation is widely used in computational aeroacoustics to postprocess unsteady simulations and provide the sound at distances beyond the accurate range of the grid. It distinguishes the monopole/dipole contributions from solid surfaces R and that from quadrupoles present in the volume of the fluid. Curle showed that at low Mach numbers, the solid-surface terms are stronger than the volume term. Very few studies have included the volume term itself, but many have used a permeable Ffowcs Williams-Hawkings surface R, which in principle surrounds the quadrupoles, giving valid results independent of Mach number; in reality for external flows, the surface cannot surround all the quadrupoles. However, in spite of doubts over the solid-surface approach even at low Mach numbers, it is widely used because of its simplicity and the difficulties associated with turbulence crossing the permeable surface. We consider Mach numbers M up to 0.25, which challenges approximations based on the property that "M (1." An additional attraction of the solid-surface approach is the idea of identifying the "true" source of the sound by computing separately the Ffowcs Williams-Hawkings integrals for different components. We wish to determine whether this "self-evident" argument gives an effective approach, and in general to assess Curle's approximations, using a sphere-dipole problem and three model problems related to landing-gear noise, namely an isolated rectangular body, a fuselage with a cavity, and one with a bluff body under it. One key test is the shielding of sound toward various directions;

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