TY - JOUR TI - Modeling of acoustic waves in pipes with impedance walls and double roots DO - https://doi.org/doi:10.7282/t3-5h7x-r570 PY - 2018 AB - Non-Hermitian systems can exhibit exceptional points (EPs) at which modes coalesce. The connection between EPs and acoustic damping goes back to the observation of Cremer (1953) that optimal attenuation in a duct occurs when the two lowest modes have equal complex-valued eigenvalues, although the physical basis for this effect remains unclear. In an attempt to understand Cremer's observation we consider the model cases of a two and three-dimensional waveguide with different impedance conditions on the boundaries. Introductory work delves into the intricacies of waveguide modeling such as solution obtaining methodologies, modal dependencies, phase velocities, group velocities, Green's function solutions, and impedance discontinuity effects. An EP existence condition is derived and explored for both cases. Doing so in this order allows for the determination of the complete set of all possible pairs of passive impedance conditions that give rise to EPs, and from these to select impedances appropriate to a particular frequency band. Numerical and computational simulations are presented to demonstrate modeling legitimacy with the inclusion of some preliminary experimental work for the purpose of establishing experiments to test physically realizable EP behavior. All results point towards promising alternatives and or explanations for large and almost perfect broadband absorption. The theoretical findings are compared to realistic passive impedance values based on models for boundary impedance. These comparisons are discussed to illustrate the feasibility of optimized wall impedances in absorbing sound passing through ducts. KW - Mechanical and Aerospace Engineering KW - Architectural acoustics LA - eng ER -