Normal mode theory for acoustic waves and its application to the interdigital transducer

A normal mode expansion for the analysis of acoustic-wave problems is given. The expansion is based on orthogonality relations between the modes of an acoustic wave, and makes it possible to relate the perturbation and propagation constant of a particular mode to the properties of the modes of the unperturbed system, and of the perturbation. The use of the general expansions is then demonstrated by using it to determine a variational expression of an interdigital transducer. The results obtained are very similar to those of Smith, and demonstrate the connection between the crossed-field and series formulations for the transducer impedance.