Calculation of the acoustical field of a semi-infinite cylindrical wave-guide by means of the green function expressed in cylindrical coordinates

The exact solution to the problem of the acoustic wave propagation is presented for a half-infinite cylindrical wave-guide with rigid walls, i.e., with taking into account the diffraction phenomena on the open end of wave-guide. The problem was solved by means of the theory of acoustic field without sources and the use is made of the Green's function method in the cylindrical space co¬ordinates, leading to two integral equations which are solvable with the help of the Wiener-Hopf method.
The wave number considered was taken to be a complex quantity, and the reduced forms of the final formulae are presented. for the limiting case of real wave number.