Wave refraction at an interface: Snell’s law versus Chapman’s law

Abstract

Energy streamlines provide insights into mechanisms of wave propagation and scattering and are often utilized to visualize wave fields. In contrast to rays, which are essentially an asymptotic, short-wave concept, energy streamlines adequately represent arbitrary wave fields. However, the usefulness of energy streamlines in studies of wave fields is limited by the fact that, unlike rays, no general laws governing energy streamline refraction are known. Here, a simple refraction law is derived for energy streamlines of acoustic and linearly polarized electromagnetic waves. It is shown that analysis of energy streamlines provides a helpful supplementary perspective on wave transmission through interfaces.

Internal Stress Monitoring of In-Service Structural Steel Members with Ultrasonic Method

“…The generated ultrasonic wave propagates from poly methyl methacrylate (PMMA) material to the steel, and then to the receiving probe via PMMA material. According to Snell’s law [34], the incident longitudinal wave angle is set as 25.7° so that Lcr wave can be generated and received. The nominal frequencies of the transducers for the probes are 5 MHz.…”

“…The other part of the energy refracts into the second medium, and the refracted longitudinal wave and shear wave are generated. According to Snell’s law [34], when ultrasonic velocity in the second medium is greater than in the first one, the angle between the refracted longitudinal wave and shear wave increases with the increase of the incidence angle of the longitudinal wave. When the incident angle increases to a certain value (different for different materials), the refracted longitudinal wave travels parallel to member surface.…”

Energy streamlines for qualitative inverse scattering in fluids and solids

“…Although complicated in some cases 28 , these paths have been found of considerable interest from several viewpoints. They can give evidence to the involved details of energy flow in wave fields 14 (even in the case of discontinuous material parameters 11,21 ), and may provide great practical advantages through applications in various problems of noise control in engineering 29 .…”