In this paper we study a particular case of the generalized d'Alembert wave equation with two independent variables, a spatial dimensionxand a temporal dimensiont,at a fixed point(x = a, t = b)of the Castelnuovo spacetime, a projective representation of the de Sitter universe that generalized Minkowski spacetime. We find a d'Alembert wave equation associated with this point, and give the complete solution for the special case of an observer at the origin of spacetime coordinates.