Higher order mode effects in circular ducts and expansion chambers

The theory of higher order modes in circular ducts is reviewed and applied to expansion chambers. Numerous schemes have been proposed for use in labeling the various higher order modes in a circular duct. This has led to confusion and, in at least one case, to erroneous descriptions of the higher order modes. In an attempt to solve this problem, a specific approach, analogous to that used in rectangular ducts, is recommended that has geometric clarity and elegance. The cutoff frequencies for these various modes are discussed with respect to propagation in an expansion chamber. Incomplete and misleading statements in the literature concerning the calculation of cutoff frequencies are reviewed. Higher order mode propagation through an expansion chamber is analyzed for various inlet and outlet locations, and experimental results presented. The interaction between plane wave and higher order mode effects is discussed.