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This paper discusses sample diffraction problems from the fields of structural acoustics in a still medium and of aeroacoustics at high subsonic Mach numbers. Respectively and specifically: Diffraction by a tandem arrangement of thin circular plates of finite radius and inertia, and scattering of high-frequency rotor/stator noise by the nacelle of a modern aeroengine. The presence of a freestream endows the elemental diffraction loads in the second class of problems with the capacity to inject vorticity into the medium. The need to account for it has classically prompted the development of a new mathematical interpretation of scattering, called ``unsteady aerodynamics,'' so that flow and flowless diffraction communities have tended to work in mutual isolation. A side objective of this paper is to speak to both groups by presenting a completely formal complex-contour representation of the fundamental lift kernel for the flow case. That spectral formulation displays the role of vorticity explicitly through an additional singularity that shifts away to complex infinity as the flow is turned off. The remaining spectrum is the Fourier transform of the hypersingular diffraction kernel of ordinary acoustics.