Diffraction of sound waves at the opening of a soft cylindrical duct

The paper presents analytical description of diffraction phenomena at the opening of an acoustically soft cylindrical duct and solution of the wave equation with adequate boundary condition imposed by the duct wall. Mathematical tools which were applied are the Green's first theorem and the Green's free-space function in cylindrical co-ordinates. As a result, the velocity potential was expressed as a surface integral, containing discontinuity of the normal component of the particle velocity on the duct wall. The solution of the problem consists in calculating this discontinuity by means of the Wiener-Hopf technique and results in formulas for the velocity potential inside and outside the duct