Analysis of the Behaviour of Standing Acoustic Waves in a Cubically Nonlinear Medium.

Abstract: The basic distinction between linear and nonlinear acoustics is given in the introductory part. The differences between nonlinear acoustic waves in quadratic and cubic media are briefly explained. The behavior of standing waves, including the wave profile evolution, is described. A perturbation analysis leading to the wave profile for a standing wave in a cubic medium is presented. Finally, interpretation of the solutions containing shock waves and verification of the matching of the inner and the outer solutions through an intermediate solution at the regions containing shock fronts are made. The plots were generated using MATLAB.