STATE-SPACE MODELING OF AN ACOUSTIC DUCT WITH AN END-MOUNTED SPEAKER

This paper develops a state space model of the dynamics of an acoustic duct with end-mounted speakers. The initial model formulation include s the forcing term as parr of the boundary conditions. The shifted par ticle velocity is then defined to transform the nonhomogeneous boundar y 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 acousti c field, which, in turn, affects the motion of the speaker cone. This interaction is studied using positive real closed-loop feedback analys is, and shifts in the modal frequencies of the duct due to the presenc e of the end-mounted speaker are predicted.