A General Reactance Theorem for Electrical, Mechanical, and Acoustical Systems

Foster's reactance theorem for the driving-point impedance of a two-terminal electric network is extended to more general cases comprising mechanical and acoustical as well as electrical systems. The network may contain distributed but finite elements besides the lumped ones. The driving force also may be distributed instead of being concentrated at a point. For the latter case, it is suggested that a quantity mass driving-point impedance is to be introduced, which has properties similar to simple impedance. Applications of the theorem to cases of practical importance are discussed.