Acoustic radiation from a multi-region impedance-lined cylindrical waveguide

This paper investigates the acoustic radiation from a semi-infinite cylindrical duct with multiple axial impedance discontinuities on the inner surface and a uniformly coated outer surface. The inner surface is divided into three consecutive impedance-lined segments, each characterized by a distinct impedance value, forming a coupled multi-region configuration. The problem is analyzed using the Wiener–Hopf technique for two geometrical configurations, namely a duct with an infinitely thin wall and a duct with finite wall thickness. For each case, the governing Helmholtz equation is reduced to a Wiener–Hopf equation via Fourier transform, and the unknown modal coefficients are determined through Dini series expansions and enforcement of the boundary and continuity conditions at each interior junction. The far-field directivity pattern is obtained via the saddle-point method. Numerical results illustrate the effects of the duct radius, frequency, segment lengths, and impedance parameters on the radiated field. The finite wall thickness formulation is shown to recover the thin wall solution in the limit b → a , and the results are validated against existing solutions in the literature.