State space modeling of an acoustic duct with an end-mounted speaker

This paper develops a state space model of an acoustic duct with end-mounted speakers. The initial model formulation introduces the forcing term as a boundary condition. The shifted particle velocity is then defined to transform the nonhomogeneous boundary condition to a homogeneous boundary condition and thus develop the state space model. It is shown that the speaker and acoustic duct interact by means of feedback in which the speaker creates an acoustic field, which, in turn, affects the motion of the speaker baffle. The interaction between the speaker and acoustic dynamics 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