Reflection of plane waves from a rigid wall and a free surface in a transverse isotropic medium

We provide a representation of the general solution to the two-dimensional equations of the dynamics of a transverse isotropic medium with the Carrier–Gassmann condition. The representation of the solution is based on two solving functions that satisfy two separate wave equations. The problem of the reflection of plane waves from a rigid wall and a free surface is solved. The reflection coefficients and transformations of plane waves are found. The obtained formulas imply the solution for an isotropic medium as well. Special cases are considered, where the forms (amplitudes) of the reflected waves are not determined uniquely but related to the form of a falling wave through a linear relation.