Mechanical and Electromagnetic Vibrations and Waves

Chapter 7

Reflection and Refraction of Waves

If a wave propagating in a medium encounters the face of another medium, it may be partially or totally reflected and a part may be transmitted across the interface. If u is the complex incident wave, the amplitudes and the phase shifts of the reflected wave u′ and those of the transmitted wave u″ are determined by the boundary conditions on the interface, which depend on the nature of the wave and the media. We define the reflection coefficient and the transmission coefficient respectively as the ratios of the complex amplitudes of the reflected wave and the transmitted wave to that of the incident wave:

Our purpose in this chapter is to study the laws of reflection and transmission of waves. We start by studying the simple case of a one-dimensional elastic wave on two joined strings and sound in two pipes connected via a membrane; then, we study the case of three-dimensional sound waves. Afterwards, we consider the reflection and transmission of electromagnetic waves on the interface of two dielectrics: a dielectric with a plasma and a dielectric with a conductor.

7.1. Reflection of an elastic wave on two joined strings

Consider two ...