Time and Frequency Responses of Spherical Source

Abstract

A symmetric spherical wave is a particular representation of sound waves propagating in a medium. A spherical source such as a point source in a limit case provides a fundamental model of sources radiating sound waves. This chapter describes the sound sources for symmetric spherical waves in terms of the radiation impedance, which explains in principle why radiated sound pressure is proportional to the acceleration of the source. Radiation impedance is a basic notion within the theory of linear systems that deal with the sound field including sound sources. The impedance function is defined using both the magnitude and phase of the transfer function. The Fourier transform of the impedance function renders the transient response of the source to an impulsive excitation in the time domain. The impulse response of a loudspeaker system may be interpreted as a representation of radiation impedance functions in the time domain.