Multiload procedure to measure the acoustic scattering matrix of a duct discontinuity for higher order mode propagation conditions

Abstract

A procedure for measuring the acoustic scattering matrix coefficients of a duct discontinuity for higher order acoustic duct mode propagation conditions is described and tested. The technique requires measurement of pressure waves per mode coming in and out of the discontinuity. Assuming N cut-on modes, the (2N)2 scattering matrix coefficients are determined after repeating the experiment for N linearly independent pressure distributions for at least two load configurations. Experiments were conducted for a straight duct and a reactive chamber. A good agreement was found between experiment and theory except near cut-off frequencies. The overdetermination method based on four loads was shown to improve the results. An analytical simulation of the experiment was developed to compute the influence on the [S] calculation of an error in temperature and total modal pressure assumed to be representative of a real measurement situation. This simulation with a discussion explains the discrepancies between experiment and theory. The test with the chamber shows that the load method fails as expected in determining the coefficients associated to the wave coming in the discontinuity from the open end side because of the property of the middle duct to filter modes making the results very sensitive to uncertainties.