Role of quasinormal modes in controlling the sound transmission loss of duct mufflers

In this work, the sound transmission of plane waves in a duct through an expansion chamber is used to illustrate the role of the quasinormal modes of the chamber in controlling transmission loss. The complex natural frequencies and mode shapes of the quasinormal modes are presented, demonstrating the loss, orthogonality, and frequency-dependent properties of the modes. We demonstrate that the expansion of the sound pressure in the chamber by the quasinormal modes is complete and that the interaction between the quasinormal modes and incident sound can be used to characterise the features of the transmission loss.