Acoustic perturbations in a parallel relativistic flow of an inviscid fluid are considered. The general expression for the frequency of the sound waves in a uniformly (with zero shear) moving medium is derived. It is shown that relativity evokes a difference in the frequencies of the sound-type perturbations propagating along and against the current. Besides, it is shown that the perturbations are not purely irrotational as they are in nonrelativistic case. For a non-uniformly (with nonzero shear) moving fluid a general set of equations, describing the evolution of the acoustic perturbations in relativistic sheared flows, is obtained and analysed when the temperature is nonrelativistic. It is shown that, like the nonrelativistic case, in the new system: (a) the excitation of vortical, transiently growing perturbations, and (b) the excitation of sound-type perturbations, extracting the kinetic energy of the background flow, are possible. It is demonstrated that the relativistic character of the motion significantly intensifies the efficiency of both these processes. Finally, the possible relevance of this study to processes in astrophysical shear flows is pointed out.