Abstract
Classic problems of reflection and refraction of sound waves on the boundary of two liquid half spaces are reformulated for more complicated and more realistic case, when acoustical properties of media change smoothly. Refraction and reflection of plane, cylindrical and spherical waves on smoothed boundaries is discussed. The propagation of waves in Pekeris waveguide with smoothed boundaries is also formulated and solutions for the point source are discussed. New formulas for rays and modes are derived for both cases.
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