Complex intensity in circular ducts containing an obstruction

Abstract

Sound intensity may be defined as a complex quantity in which the real part of the intensity is related to the magnitude of the local mean energy flow, and the imaginary part to the local oscillatory transport of energy. By treating intensity as a complex quantity it is possible to visualise energy flow in a different way and this has the potential to aid in the interpretation of, say, sound fields scattered by objects. Accordingly, the sound field scattered by an object placed in a semi-infinite circular duct is examined here. Experimental measurements of complex intensity are obtained in three (orthogonal) directions using a Microflown intensity probe, and measurements are compared to predictions obtained using a finite element based theoretical model. Comparisons between prediction and measurement are undertaken for both plane wave and multi-modal sound fields and here it is noted that when at least one higher order mode propagates it becomes more difficult to obtain good agreement between prediction and experiment for the complex intensity.