Decay rates and related transport coefficients of hydrodynamic disturbances in the isothermal dissipative particle dynamics (DPD) fluid depend strongly on how the probing wave length (in simulations: sizes of colloidal particles, polymers, pores, etc.) compares to the dynamic correlation length and to the range of the DPD forces. In this article the wave number dependent transport properties (dispersion relations) of the DPD fluid are calculated analytically using methods of kinetic theory, as a natural generalization of the work by Marsh [Phys. Rev. E 56, 1976 (1997)]. The Navier-Stokes transport coefficients are recovered in the hydrodynamic limit of long wavelength disturbances.