Scalar wave analysis of distributed and moving sources by means of Huygens construction

The present paper presents several applications of wave front construction associated with stationary distributed and moving point sources. The scalar wave equation which is used models both isotropic and anisotropic media, in which the displacement is parallel to an axis of symmetry and is independent of distance along the axis. The stationary sources are distributed along parabolic and hyperbolic curves, while the point source is subjected to both uniform and accelerating motion along a straight line, uniform motion around a circular path and back and forth motion along a straight line. The wave fronts are constructed explicitly by the method of envelopes and special attention is paid to the formation of cusps on the wave front. If the method presented here for wave front analysis is carried out in advance, then one can gain a better insight into expected motion behind the wave front.