Solutions of the inhomogeneous wave equation for sources on an expanding and moving disk are discussed. An algorithm for constructing these solutions in terms of modes of the cylindrical coordinate system is given. We demonstrate how to use them in the special case where sources move with the velocity of wavefront and expand with a velocity that is less, equal or greater than the wavefront velocity. A family of ``superluminal'' solutions is obtained. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.