On the representation of cavity fields in terms of laterally guided waves

Abstract

Lateral-wave representation of forced acoustic oscillations in a homogeneous gas contained within a perfectly rigid cavity are compared for two cases that differ only by the presence in one case of a rigid inner core in addition to the rigid outer shell of the cavity. The two representations exhibit increasingly similar laterally propagating modes as the core of the one case is made smaller relative to the wavelength of the oscillation, although significant differences persits near the mode cutoffs. When the core is present, the propagating modes are accompanied by a discrete spectrum of evanescent lateral modes. The evanescent modes become increasingly dense as the size of the core is reduced, to be replaced entirely by a continuous evanescent spectrum in the absence of the core. This continuous spectrum, which is shown in the present instance not always to be negligible, arises mathematically in a manner similar to the “background” continuum found in lateral-wave decompositions of the scatter of acoustic waves from penetrable cylinders and spheres.