Abstract
Assuming that the variations of wind speed and sound speed are significantly less than the speed of sound close to the ground, the first and the second approximations of ray equations have been derived. The first approach yields the parabolic shape of a ray when the linear dependence of wind speed and sound speed upon height is assumed. In the instance of nonlinear dependence, the generalization of Ingard’s formulas, which determines the slant distance between the source and shadow boundary, is given. Both cases of linear and nonlinear shadow boundaries are defined by grazing rays when specific conditions are met.
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