XL.Accession to inertia of and power radiated by a sphere vibrating in various ways; with applications to hornless loud speakers

Abstract

Abstract By aid of zonal spherical harmonics (Legendre's functions) formulæ are deduced for the accession to inertia of, and the power radiated from, a sphere or a hemisphere vibrating in various ways. Cases are chosen which have a direct bearing on hornless loud-speaking apparatus, and the results applied thereto. The influence of constant driving force at all audio-frequencies is considered for several modes of vibration. It is deduced that under certain conditions a radially vibrating sphere gives perfect reproduction of acoustic pressures. The increase in low-frequency output due to a large baffle is calculated for disks and spheres. When two diaphragms vibrate in opposition along a common axis, it is indicated that a baffle is unessential provided the useful radiation is confined to the external surfaces of the vibrators. The accession to inertia of, and the power radiated from, a sphere having nodal circles is treated by means of sectorial harmonics. The low frequency radiation decays with amazing rapidity with increase in the number of nodal circles. This arises from interference due to oppositely vibrating segments. It follows that the L.F. interference concomitant with free-edge disks or conical diaphragms executing diametral modes is extremely large, provided the system is substantially symmetrical. By aid of formulæ given in the analysis the mechanical impedance of various types of spherical vibrator can be found.