Propagation and radiation of sound from flanged circular ducts with circumferentially varying wall admittances, I: Semi-infinite ducts

The propagation of acoustic waves in an infinite circular duct with a circumferentially varying wall admittance is theoretically considered. An exact solution is obtained and used to investigate the characteristics of wave dispersion, mode shapes and admittance. The scattering from a flanged termination of the circular duct is then analyzed with use of a rigorous solution in oblate spheroidal co-ordinates. The effects of the asymmetry of the duct wall admittance on the amplitude reflection coefficients, radiated power transmission losses and the far field radiation directivity patterns are examined.