The spectral analysis of a single wave measurement (for instance strain measurement) on a rod exhibits multiple resonant frequencies. Wave celerity is inferred from the resonance position and attenuation is deduced from the resonance bandwidth. Dispersion is therefore computed on a countable set of frequencies. This method does not need any limitation of the loading pulse. When applied to an aluminium rod, the method allows for the measurement of the damping and the dispersion relations for a frequency range up to 50 kHz. It is found out in this case that damping is non zero. Results are checked using the wave propagation description in a real rod. They show to be of a high accuracy. This method can be applied to any one-dimensional and single-mode propagating waves (for example flexural waves in beams).