A double elastic panel, set in a light compressible fluid, is excited by a time harmonic force applied along a line on one of the plates. The double panel consists of two parallel elastic plates, with different elastic properties, each of width a and separated by distance d≪a, set in rigid plane baffles with acoustically soft adjoining side walls. Each plate is taken to have infinite extent in the z-direction, so that the problem treated is a two-dimensional one. The radiated acoustic power is estimated asymptotically, averaged over a small frequency band and over all line force positions, for frequencies that are sufficiently high to ensure the excitation of many panel modes, with ka≫1 and kd >> 1, where k is the acoustic wave number. Transition formulae are given for frequencies ω that are near to either of the coincidence frequencies, ω1 and ω2, of the individual panels.