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This study focuses on sound attenuation in a two-dimensional waveguide with arbitrary admittance boundary conditions on both sides of the guide. The emphasis is on understanding the formation and potential applications of the exceptional points (EPs) which arise when two (EP2) or three (EP3) modes degenerate into a single mode. A perturbation approach is used to obtain asymptotic expressions for the trajectories of the axial wavenumbers in the complex plane as they coalesce to form an EP. The numerical results presented herein suggest that the first triple root (EP3) assures maximum modal attenuation along the waveguide. Further, it is demonstrated that the classical Green's function is degenerate at an EP. Modified Green's functions which are valid at EP2 and EP3 are presented. [ABSTRACT FROM AUTHOR]