Assessing precision and accuracy in acoustic scattering matrix measurements

Acoustic scattering matrices are used to characterize the influence of inline duct elements on the acoustic wave propagation in wave guides.When measuring the properties of these matrices, errors are always present in the results and need to be characterized to make valid statements on the correspondence between model predictions and measurements.In this study the random and systematic errors in acoustic scattering matrix measurements are investigated.Several aspects of the measurement cycle are examined, starting with the determination of the random error on the measured transfer functions between the acoustic source signal and the measured acoustic pressure.The second aspect is the determination of the random error on the scattering matrix coefficients. They are mathematically derived from the measurement data and the error has to be propagated from the data to the coefficients.This is done using uncertainty analyses and the use of linear methods to calculate the uncertainty of the coefficients is investigated.The impedance tube is an essential element of acoustic scattering matrix measurements and the third topic is a description of the systematic errors that can occur in these tubes. The effect of various systematic errors are shown, together with methods to account or reduce them.It is shown that there are still systematic errors remaining, and hypotheses to the source of these errors are discussed.In the last part, the knowledge is put to use to measure the aero-acoustic interaction present at a sudden area expansion.It is shown that the measured acoustic absorption agrees qualitatively with the models, however the deviation between the measurements and predictions are larger than the uncertainty of the measurements.The end correction agrees well with the models at high Strouhal numbers, but the scatter on the measurements at lower Strouhal numbers is too large to identify flow-acoustic interaction effects on the end correction.QC 20170508TANG