Green function analysis of the acoustic field in a finite three-port circular chamber

Abstract

Abstract The velocity potential which expresses the acoustic fields in a three-port circular duct (one source port being located on the cylindrical wall, a second one being situated on the circular but flat surface at one end and the third passive port being the circular flat surface at the other end, assumed to have frequency dependent generalized wall impedance), is obtained based on a Green function which satisfies the linear acoustic wave equation and homogeneous boundary conditions. The boundary conditions are assumed to be rigid except for the active source ports and the passive termination. The Green function is derived in terms of the frequency dependent orthogonal eigenfunctions which satisfy frequency dependent termination impedance boundary conditions. To illustrate the potential value of the solution, the modal density, acoustic potential energy distributions and the modal participations along the duct are examined for the open end and anechoicic termination cases. The possibility of using the solution for the determination of the positions of detection and error microphones in an active noise control system is also discussed.