Statistical errors in the estimation of time-averaged acoustic energy density using the two-microphone method

Abstract

<jats:p>Time-averaged acoustic energy density can be estimated using the auto- and cross-spectral densities between two closely spaced microphones. In this paper, an analysis of the random errors that arise using two microphone measurements is undertaken. An expression for the normalized random error of the time-averaged acoustic energy density spectral density estimate is derived. This expression is verified numerically. The lower and upper bounds of the normalized random error are derived. It is shown that the normalized random error of the estimate is not a strong function of the sound field properties, and is chiefly dependent on the number of records averaged.</jats:p>