The problem of sound propagation over a flat plane with a line of impedance discontinuity is considered. The sound excitation source is assumed to be linear and set parallel to the line of impedance discontinuity. The solution to this problem is formulated by considering the plane wave spectrum decomposition of a cylindrical source, this is incorporated in the solution to the problem of plane wave diffraction by a wedge with different face impedances. The propagation over a plane surface is then taken as the special case of a wedge whose angle is equal to 180o. The present solution is, however, a high frequency asymptotic formulation, and comparisons are therefore made with two other available models, approximate also, but using instead a point-like sound source. A practical application of the present study would include the evaluation of the insertion loss of a noise barrier on a ground with different acoustical properties on either side of the barrier. The properties of the sound field above the ground may be studied prior to erecting the noise barrier at the line of impedance discontinuity.