An improved approximation for wave propagation above an impedance ground in a medium with a linear sound-speed profile

Abstract

The atmospheric profile whose sound speed varies linearly with height is simple in concept, but leads to complications when solving for the sound pressure. Its effects are commonly approximated by a similar profile whose squared refractive index is a linear function of height. In this paper, the validity of the approximation has been examined for sound propagation above an impedance ground and an improved approximation is given. The new approximation is based on a WKB-type analysis using Airy functions as the general solution to the wave equation. Numerical examples show that this new approximation more adequately models the sound field for the linear sound-speed profile for a wide range of detector heights and gradients and for both upward and downward refracting atmospheres.