Analysis of the interaction between cascade sub-chambers using the acoustic scattering matrix method

Cascade structures are widely used in the design of reactive silencers. Previous studies have demonstrated that a broadband transmission loss (TL) can be achieved via an optimal design for the cascade sub-chambers of the structures. Although the TL of each sub-chamber can be estimated, the overall transmission loss of the silencer is not simply a summation of the TLs of the sub-chambers. The acoustical coupling between sub-chambers must be taken into account. The scattering matrix method is used to evaluate the contribution of each sub-chamber to the TL of the silencer. The method is illustrated numerically using 2D examples, which can be extended to 3D cases in straightforward manner.