Ray and diffraction effects of acoustic waves when atmospheric conditions produce nonlinear acoustic velocity profiles

Abstract

The propagation of acoustic pulses in a medium with refractive index n=(a+be−αz)ν, where a, b, ν, α are constants, is discussed within both the ray and diffraction analysis. This work is of relevance to the propagation of acoustic pulses in media which have temperature gradients and/or wind gradients. It is shown that both treatments are amenable to exact solution. A new class of analytical solutions are presented that are of relevance to scientists working in the area of wave propagation in the atmosphere. In the ray treatment a generalization of the linear gradient is obtained that suggests greater bending as compared to the linear case, while in the diffraction limit, the solutions of the wave equation are shown to be particular examples of confluent hypergeometric and Papperitz functions. Qualitative discussions of the solutions are presented.