Self and mutual radiation impedances between translated spheroids. Application to parallel disks

This article derives the radiation impedance for two parallel pistons in two different configurations: baffled and unbaffled. For the former, the cylindrical system of coordinates is adapted to compute the self and mutual impedance of a piston between perfectly rigid infinite parallel planes. For the latter, spheroidal coordinates are used and declined for the case of two disks in free-space. The formulae for Green's function that respects Neumann boundary conditions are established in both configurations in order to compute the pressure field using the Huygens-Fresnel principle. Contrasting with the radiation impedance obtained for one single radiator, both systems exhibit resonant frequencies. The result of this study, validated in each case by a numerical method, can be used to predict the acoustic interaction of two vibrating systems for which their radiation surfaces are facing each other.