We consider the propagation of sound in a two-dimensional shear layer in a duct. Initially plane sound waves propagate in a subsonic flow whose steady velocity U(y) is in the axial direction and is a function of the normal co-ordinate alone. The initial-value problem in time and space is solved within the framework of a perturbation scheme. Far from the wave front and for large time the refractive effects are considerable. However, the present results indicate that standing wave type patterns lead to a strong dependence on axial location in the duct. The paper also points out the Weakness inherent in theories which attempt to treat the refraction problem without considering the source conditions.