Radiation of sound waves from a rigid stepped cylindrical waveguide

The radiation of plane harmonic sound waves from a rigid stepped cylindrical waveguide is treated by using the mode-matching method in conjunction with theWiener-Hopf technique. The solution is exact, but formal, since infinite series of unknowns and some branch-cut integrals with unknown integrands are involved. Approximation procedures based on rigorous asymptotics are used and the approximate solution to the Wiener-Hopf equations is derived in terms of infinite series of unknowns, which are determined from infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the directivity of the stepped waveguide is presented.