ABSTRACT
The closed sphere is the simplest three-dimensional scatterer of finite extent. Both acoustically hard and soft spherical surfaces have been intensively studied in all wavelength bands: the low frequency or long wavelength regime, the intermediate or resonance regime, where the scatterer around one or a few wave lengths in size, and the high frequency or optical regime. This chapter examines perhaps the simplest three-dimensional cavity structure: the thin spherical shell with a circular aperture. The shellmay be acoustically soft or hard, and is illuminated by an acoustic plane wave. The chapter discusses the mathematically rigorous description, concerning diffraction by a circular hole in an acoustically hard spherical shell, to construct a rigorous theory of the spherical Helmholtz resonator. From a physical point of view it is reasonable to postulate that all the kinetic energy of the system is concentrated in the column of air that moves in the tube as a plunger.
