### ASA 130th Meeting - St. Louis, MO - 1995 Nov 27 .. Dec 01

## 3aPAb11. An improved approximation for sound propagation in a medium with a
linear sound-speed profile.

**Michael J. White
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*U.S. Army Construction Eng. Res. Lab., P.O. Box 9005, Champaign, IL
61826-9005
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**Y. L. Li
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*Univ. of Illinois, Urbana, IL 61801
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**Jianfeng Tai
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*U.S. Army Construction Eng. Res. Lab., Champaign, IL 61826-9005
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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.