A theory is presented that describes the formation of the discrete radio tones that could apply to the radio emission observed in the outer heliosphere by the Voyager spacecraft. Specifically a broadband emission is assumed to be trapped within the heliospheric cavity. If the heliospheric outer boundary, the heliopause, has a large-scale, monochromatic oscillation, the trapped emission will form intense, discrete tones at wave frequencies where the photon travel time is an integer ratio of the boundary oscillation period. A new set of nonlinear coupled difference equations are presented that describe the interaction of the trapped photon with the boundary, the set appearing similar to that used to model Fermi acceleration of particles via oscillatory boundaries. Results indicate that heliopause oscillation periods on the order of 1000s of seconds could generate tones at frequencies near those observed by Voyager. The tones can also drift in association with the changing cavity size of oscillation period. ¿ American Geophysical Union 1993