Transfer function method of measuring in-duct acoustic properties. I. Theory

The theory of a transfer function method of measuring normal incident in-duct acoustic properties is presented. In this method, a broadband stationary random acoustic wave in a tube is mathematically decomposed into its incident and reflected components using a simple transfer-function relation between the acoustic pressure at two locations on the tube wall. The wave decomposition leads to the determination of the complex reflection coefficient from which the complex acoustic impedance and the sound absorption coefficient of a material and the transmission loss of a silencer element can be determined. Also presented are the theories of two techniques for improving transfer function estimates: a sensor-switching technique for automatic system calibration and a coherence function technique for signal enhancement.