Mutual Acoustic Impedance between Flexible Disks of Different Sizes in an Infinite Rigid Plane

Abstract

A direct method of analysis based on the “classical” Rayleigh formula is presented for calculating the mutual acoustic impedance between circular radiators of different sizes in an infinite rigid plane. The effects of the interactions between two radiators are considered in detail. The acoustic pressure on the plane baffle is described by a distribution of surface “sources” of known strength at the plane-fluid boundary. As the sound-pressure field produced by one radiator exerts a force on another radiator on the plane, the mutual radiation impedance can be defined by the force exerted by one radiator integrated over the surface of the other. This impedance is expressed by a series solution of products of Bessel functions. The results can be reduced to those found by Pritchard and Porter, who based their solutions of the problem as formulated by Bouwkamp. Numerical calculations for the series solutions of the pressure field and of the mutual impedance terms are not given. Attention is paid only to mathematical formulisms.