A rigorous analysis presented of the excitation of sound by point sources moving in uniform translatory motion at subsonic or supersonic velocities through a two- or three-dimensional medium at rest. The construction of surfaces of constant phase is based upon Huyghens' principle in such a manner that the propagation in the medium at rest of the elementary waves emanating from the sound source is independent of the momentary state of motion of the sound source. Hence, characteristic traits of the sound propagation may be understood even on the basis of simple geometric constructions.