Exact solution for guided sound transmission through a double partition

The exact solution is obtained for the problem of the transmission of a symmetric sound wave through a double partition contained in a parallel-plane waveguide with rigid walls. A membrane model is used for the two leaves of the partition. The solution involves a number of infinite series which converge rapidly. It is not necessary to make any special assumptions regarding the parameters describing the model. In particular no modifications are necessary for the region of the critical frequencies. Full details are given for the particular case of an incident plane wave. The result, which is suitable for computation, involves four converging infinite series. In general there are no frequencies of complete transmission or reflection. Similar analysis applies to the case of a circular waveguide.