Analysis of the uncertainty budget for the reflection and absorption coefficient given by the two-microphone method

Abstract

The method for measurement of the reflection and absorption coefficient at normal incidence consists of a sound source at one end of an impedance tube, where the plane waves propagated are reflected from a sample that is at the other end of the tube. Those plane waves are generated by a random signal, and the decomposition of the standing wave pattern is carried out measuring the acoustical pressure at two-fixed microphone positions, from which it is possible to determine a transfer function to obtain the reflection and absorption coefficient. The systematic errors associated with the two-microphone technique using an impedance tube are analyzed, i.e., microphone-sample distance, microphone spacer, atmospheric measurement conditions, correction factors to the microphone sensitivity, and phase and amplitude mismatch in the microphones. These parameters constitute some of the sources to the measurement uncertainty of the measurand-reflection and absorption coefficient. The estimation of the measurement uncertainty for the reflection and absorption coefficient by the two-microphone method; likewise the analysis of the uncertainties sources and its sensitivity coefficients are discussed using a linear approach model. Furthermore, the influence of the correction factor due to the frequency response mismatch in the microphones in the calculation of the reflection and absorption coefficient is experimentally evaluated.