Michael J. White
U.S. Army Construction Eng. Res. Lab., P.O. Box 9005, Champaign, IL 61826-9005
Y. L. Li
Univ. of Illinois, Urbana, IL 61801
U.S. Army Construction Eng. Res. Lab., Champaign, IL 61826-9005
The use of a refractive index profile whose square varies linearly with height is a common approximation when solving for the sound propagation in a refracting atmosphere. Its solutions are more tractable than those for an atmosphere whose sound speed varies linearly with height, although the linear sound-speed profile is more often the one whose solution is sought. In this paper, the approximate relationship between the two profiles has been examined. Numerical examples show that the two profiles give similar solutions for the sound pressure only when the background atmosphere is upward refracting. When the atmosphere is downward refracting, however, the two profiles give results that disagree except when the refraction is extremely small. In this paper, an improved approximate solution for the pressure field is given for the linear sound-speed profile. The solution is based on a WKB-type approximation which uses Airy functions as the general solutions of the wave equation. Numerical comparisons are made to show that the new approximation 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.