Post-processing the strain waves in split Hopkinson pressure bars to get the stress-strain in the sample requires the knowledge of the characteristic wave speed c0 in the measuring bars. In the context of metrology, the measurement uncertainty in the value of c0 must be assessed. The aim is to minimize this uncertainty, which depends on the way c0 is determined, as it has an impact on the uncertainty in the final stress and strain in the sample. The frequency domain method we introduce is based on an impact test on a single bar. The frequency spectrum of the impact response of the bar clearly exhibits the longitudinal resonant frequencies of the bar. The experimental dispersion curve is deduced from the spectrum and an optimization procedure was applied to determine the wave speed c0 along with the Poisson's ratio and the uncertainty in the wave speed. This method gives a relative uncertainty in c0 lower than 0.05%: it is mainly related to the uncertainty in the length of the bar (which is hard to reduce when using standard meter tape), which prevails over the uncertainty in the resonance frequencies of the bar. A precise value of the wave speed c0 and of the associated measurement uncertainty is an important step in the context of split Hopkinson pressure bars if we want to precisely assess the final uncertainty in Split Hopkinson pressure bars test results, which is at present scarcely done.