Analogy between the one-dimensional acoustic waveguide and the electrical transmission line in the cases of nonlinearity and relaxation

The propagation of plane acoustic waves can be investigated by taking advantage of the electro-acoustical analogy between the one-dimensional acoustic waveguide and the electrical transmission line, because they share the same type of equation. This paper follow the previous studies and expand the analogy into the cases of quadratic nonlinearity and dispersion produced by relaxation process. From the basic equations relating acoustic pressure, density fluctuation and velocity, which are valid for the nonlinear and relaxing media, the equivalent travelling-wave circuits of one-dimensional acoustic waveguide with the consideration of nonlinearity and relaxation processes are obtained. Furthermore, we also discuss the analogy relationship of parameters which exist in the acoustical and electrical systems.