A General Theory of Passive Linear Electroacoustic Transducers and the Electroacoustic Reciprocity Theorem. I

Abstract

A theory of the operation of passive linear electroacoustic transducers is developed on the basis of the most general linear equations (in this case, integral equations) relating the pressure and normal velocity at each point on the transducer surface and the voltage and current at the transducer's electrical terminals. These, together with the appropriate solutions of the wave equation expressed through the use of Green's functions for the medium in which the transducer is immersed and the equations defining the electrical termination of the transducer, completely characterize the behavior of the transducer and allow explicit calculation of such quantities as impedances, responses, etc., in terms of four parameters entering the fundamental equations. On the basis of this theory, a proof of the reciprocity theorem for electroacoustic transducers relating their speaker and microphone responses is presented embodying the conditions necessary for its validity. These conditions are essentially the existence of certain symmetry relationships among the transducer parameters. When these symmetry relationships may be expected to hold is to be discussed in Part II of this paper to appear later. Some applications of the theory are presented and others are outlined.