State Space Modeling of an Acoustic Duct With an End-Mounted Speaker

Abstract

This paper develops a state space model of the dynamics of an acoustic duct with end-mounted speakers. The initial model formulation includes the forcing term as part of the boundary conditions. The shifted particle velocity is then defined to transform the nonhomogeneous boundary conditions into homogeneous boundary conditions and thus develop the state space model. It is shown that the speaker and acoustic dynamics interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker cone. This interaction is studied using positive real closed-loop feedback analysis, and shifts in the modal frequencies of the duct due to the presence of the end-mounted speaker are predicted.