Reflection of acoustic waves from a continuously varying interfacial region

Reflection‐transmission problems for plane waves can be analytically solved in a restricted number of special cases for which asymptotic connection formulas exist. The technique is demonstrated for the case of a parabolic barrier. A method of Epstein's, which makes use of the properties of hypergeometric functions, can be used to obtain solutions for a variety of transitional structures. This method is taken from the field of ionospheric radio‐wave propagation and is adapted to the acoustic problem without neglect of the density gradient. The solution for a monotonic transitional zone is obtained, and the behavior of the subcritical reflection is discussed, with reference to the inner core reflection as an example.