Theory of Sound Propagation in a Duct with a Branched Tube Using Modal Decomposition

The present paper extends the scope of a previous paper of one of the authors [1]. The modal decomposition is used to obtain both an exact result in a matrix form and a variational formulation for the description of the insertion of a branched tube on a main waveguide where only the planar mode propagates. Two representations are given: a two-port junction and a three-port junction, with their equivalent circuits. Results are given for the 2D, rectangular geometry case, with a discussion of some approximations and convergence problems. Concerning the circular geometry, new formulae are given and compared with results determined with the boundary element method.