A comment on the correct boundary conditions for the Cremer impedance.

Mode merging and the creation of exceptional points can be used to create optimum damping in a lined duct, as pointed out by Cremer [Acustica 3, 249-263 (1953)]. The effect of a mean flow has traditionally been analyzed by assuming the Ingard-Myer boundary condition at the wall. For low frequencies, however, the classical boundary condition is a better alternative. This paper shows that this choice removes two problems with the low-frequency solution: the negative real part of the optimum wall impedance and the non-valid solution for the upstream case. Theoretical derivations are complemented by numerical results to support these conclusions.