Transmission of high frequency sound waves through a slug flow jet

An analysis has been performed of sound waves which propagate in a pipe with gas flow. At the pipe exit these waves are partially reflected and the remainder are diffracted. The analysis is carried out by resolving the sound at the exit into its Fourier components and then continuing the solution, which is a combination of elementary plane waves, beyond the exit. These waves are of two types: homogeneous waves which propagate to infinity, and inhomogeneous waves with complex wave numbers which decay. The reflected waves are evaluated from the inhomogeneous waves. At the boundary of the jet, refraction of the elementary plane waves is accounted for and the far field sound is evaluated by the method of stationary phase. Comparisons of the theoretical calculations are made with experimental results and with calculations of other theories.