An analysis is made of the scattering of bending waves at the edge of an unbaffled, thin elastic plate in the presence of arbitrary fluid loading. Detailed predictions are made of the sound scattered from free and clamped edges, and empirical formulae given for the radiation loss factor over a range of frequencies and fluid loadings. Application is made to the generation of sound by an aerodynamic dipole source adjacent to a finite plate, a finite length of which has been treated with damping material. The dipole models the production of sound by blade-vortex interactions occurring when turbulence or discrete vortices are ingested by a ducted rotor, in which the plate assumes the role of a neighbouring duct wall. In typical underwater applications, when the influence of fluid loading is important, sound produced by the source at frequencies below the coincidence frequency of the bending waves can propagate directly to the far field, essentially as if the plate were absent. However, flexural plate-motions are also generated by the source. These contribute to the radiation by scattering at the edges and, in the absence of dissipation in the plate, the intensity of the edge-scattered sound can dominate the direct radiation from the source. When the edges can vibrate freely, it is shown that a relatively modest amount of damping is sufficient to reduce the edge generated sound to levels below those of the direct radiation. The efficiency with which bending wave energy is converted into sound is much larger for clamped edges, and larger values of coating loss factor and length are necessary to achieve significant reductions in the structural component of the radiated sound.