Mathematical modelling of acoustic transmission lines containing elements which can be represented by their acoustic modes is considered. Of particular interest are tapered elements and acoustic cavities which operate at frequencies above which a simple volume expansion representation or a plane wave representation is adequate. An element matrix formulation is given which is suitable for inclusion in the Acoustic Wave Finite Element assembly procedure, or with suitable modifications, to the more traditional transfer matrix approach. Numerical examples are provided demonstrating the accuracy of the procedure.

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