Propagation of sound in an infinite two‐part duct carrying mean flow inserted axially into a larger infinite duct with wall impedance discontinuity

The propagation of sound in a two-part circular cylindrical duct carrying a mean gas flow, inserted in a larger infinite outer duct with wall impedance discontinuity is investigated rigorously through the Wiener-Hopf technique. The part z 0 is perforated. The related matrix Wiener-Hopf equation is first transformed into two simultaneous equations which are decoupled by the introduction of infinite sum of poles. The exact solution is then obtained in terms of the coefficients of these poles satisfying two infinite systems of linear algebraic equations. The influence of the outer duct radius, the contrast of the lining impedances, the mean flow, and the acoustical impedance of the central perforated tube on the sound propagation are displayed graphically.