The solution of the homogeneous wave equation is revisited, under two criter'ia: (a) No mathematical solutions are discarded a priori, and (b) The solution by  eparation of variables is done without decoupling time and distance. Three groups of nonconventional components are identified: (1) Two non-dispersive terms in Cartesian coordinates, (2) New directional solutions in spherical coordinates, and (3) New time-distance solutions in spherical coordinates which amount to closed three- dimensional travelling waves.