The energy distribution in the far field radiated from the semi-infinite unflanged cylindrical wave-guide

The theory of an arbitrary axi-symmetric Bessel mode in a circular wave-guide is reviewed and applied to the analysis of the energy distribution in the far field outside the duct. The duct is assumed to be semi-infinite and perfectly rigid, and the diffraction phenomena occurring at the open end are taken into account. The intensity directivity function as well as the power-gain function for every mode appearing in the duct, with the diffraction parameter ka changing within the limits 0-15, has been discussed. The formulae for the intensity directivity function were derived by applying the saddle point method to the exact expression for the acoustic velocity potential. The first and second approximations are developed and the results of computed numerical characteristics are discussed.