ABSTRACT
Up to now, we have been studying the propagation of ultrasonic waves in an unbounded medium. At the boundary separating two media a wave is partially reflected, interfering with the incident wave, and partially transmitted into the second medium. In this chapter, we shall determine the criteria for the reflection and transmission of plane waves under different conditions of oblique and normal incidence on the boundary between two media, and we shall study the structure of the interference field formed when the reflected wave is superposed on the incident wave. For the time being, we shall confine our attention to media which support only longitudinal waves, i.e., liquids and gases, since the results obtained also hold for other types of waves. At boundaries between solid media, in addition to being reflected and refracted, waves are also transformed from one form into another (see below), but the general energy balance and the laws of reflection and refraction remain the same for each wave. We shall confine our attention below to monochromatic plane waves with infinitesimal amplitude, taking into account the role of nonmonochromaticity, nonlinear effects, and attenuation in the adjacent media. The results which we shall obtain for these waves are generally also valid for waves with other configurations (spherical, cylindrical, etc.) with respect to their rays, i.e., normals to the wavefront. For this reason, we shall not study specially the transmission of spherical and cylindrical waves and waves of other configurations through a boundary, but rather we shall take into account any corrections attributable to differences in the angles of incidence. We shall start the analysis of the transmission 173of plane waves through the boundary between two media with the simplest cases, generalizing the results later to more complicated situations. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429332227/64e5e3df-c95f-4a2a-a02e-98ef4c2d440f/content/fig7_37.tif"/>
