Reflection and Refraction of Harmonic Plane Acoustic Waves by a Plane Interface of Media with Arbitrary Acoustic Properties

Abstract

We propose universal formulas for the amplitudes of longitudinal and transverse plane acoustic waves, which are reflected and refracted by a plane interface of two media. The formulas are valid for liquid and gaseous media, as well as for elastic isotropic media. Advantages of these formulas are their relative clarity compared with the well-known and commonly accepted formulas, as well as a possibility to pass over from one scattering problem to another by simply replacing the corresponding wave numbers. Despite the well-known methods which are used in the calculations and rather have a methodical character, we manage to find a new type of surface waves at the interface of elastic media. These waves are characterized either by ratios of the wave numbers of transverse waves and densities, or by only the wave numbers of longitudinal waves and the ratio of the densities of media.