Determination of energy density in ducts by a three-microphone phaseless method and estimation of measurement uncertainties

A new method to measure the total energy density of waves traveling in opposite directions in ducts is suggested in order to completely eliminate phase errors that lead to bias errors and are difficult to control in industrial tests. Only the auto-power spectral densities are measured by the three microphones. The inversion of a linear system based on a propagation model, where the two opposite waves are partially coherent, makes it possible to obtain the energy density. The sensitivity of this method to errors in the speed of sound, errors of microphone calibration and errors of microphone positions in the duct is analyzed. To complete the study on the robustness of the method, an evaluation of the statistical errors is carried out. The total uncertainty is used to make recommendations on the choice of the experimental parameters. The selection of the frequency limits permits to maintain the measurement uncertainty within a given confidence interval.