On the statistical errors in the estimate of acoustical energy density by using two microphones in a one dimensional...

It was recently shown that the statistical errors of the measurement in the acoustic energy density by the two microphone method in waveguide have little variation when the losses of coherence between microphones increase. To explain these intervals of uncertainty, the variance of the measurement is expressed in this paper as a function of the various energy quantities of the acoustic fields--energy densities and sound intensities. The necessary conditions to reach the lower bound are clarified. The results obtained are illustrated by an example of a one-dimensional partially coherent field, which allows one to specify the relationship between the coherence functions of the pressure and particle velocity and those of the two microphone signals.