The sound field behind a circular disk in the presence of a point source of sound on its axis, is computed approximately. The calculation is based on the reduction of the Kirchhoff surface integral to a line integral by the Maggi Transformation. The predictions of the Kirchhoff theory are compared with a more accurate calculation which makes use of the Green's function. The theory is compared with accurate measurements of the sound field, and satisfactory qualitative and quantitative agreement is found.