The farfield pressure radiated by a force‐excited, extensive plate, separated from an ambient liquid by an air bubble swarm, is expressed in closed form in terms of bubble swarm and plate parameters, frequency, and the spherical angle ϑ from the normal to the plate. Comparing the pressure field with that of the plate in the absence of the bubble swarm, a ϑ‐dependent insertion loss is computed. The wavenumber and impedance of the bubble swarm being highly dispersive, simple asymptotic expressions giving the insertion loss are formulated for various frequency ranges.