Title: Analysis of the Behaviour of Standing Acoustic Waves in a Cubically Nonlinear Medium
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.
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Author: Chinenye Igweokpala, Onyema Umegboro
Source: Blekinge Institute of Technology
Contents
1 Notations
2 Introduction
2.1 Some common applications
2.2 Quadratic nonlinearity versus Cubic nonlinearity
3 Physical background and analysis of standing wave in cubic nonlinear medium
3.1 Free Standing waves
3.2 Forced Standing waves
3.3 Forced shocked waves
3.3.1 The mean intensity is greater than discrepancy
3.3.2 The mean intensity is equal to the discrepancy
3.3.3 The positive discrepancy is greater than the mean intensity
3.3.4 The positive discrepancy is greater than the mean intensity
4 Perturbation solutions to the equation with cubic nonlinearity
4.1 Graphical Analysis of the equation with cubic nonlinearity
4.2 Matching of the inner to the outer solutions using an intermediate solution at shock regions.
5 Conclusion and Discussion
6 References
7 Appendices