Acoustic eigenmodes of corrugated ducts

Acoustic propagation in two-dimensional corrugated ducts is analyzed. A transform is made to a coordinate system that matches the duct walls. The resulting wave equation separates in space and time. The spatial differential equation is then solved by expanding in the eigenfunctions of a flat-walled duct. The prescription for this expansion is given by the appropriate application of time-independent perturbation theory. Calculations of first-order corrections for sinusoidal ducts of finite and infinite length are presented. A general conformal transform for symmetric ducts of arbitrary cross section is also included. [This work was supported by NASA Lewis Research Center under Research Grant NGR 22-009-805.]