# Physical Basis for Ultrasonic Acoustics

## Abstract

This chapter presents a review of the physical basis of ultrasonic waves in elastic media and bimaterial interfaces. The chapter gives an overview of the description and presentation of the wave propagation problem, which can become quite complicated in some cases. The chapter starts with discussion of the wave propagation equation in an infinite elastic medium. The general equations of 3-D wave propagation in unbounded solid media are developed from first principles. The eigenvalues and eigenvectors of the wave equation are identified. The two corresponding basic wave types, *pressure waves* and *shear waves*, are discussed. Dilatational, rotational, irrotational, and equivolume waves are identified and discussed. The case of *z*-invariant wave propagation is presented.

Bulk wave interaction at bimaterial interfaces is presented next. The solid-solid interface is studied first. The interface conditions are set up in terms of potentials and the coherence condition (aka Snell’s law for ultrasonics) is derived. The general solution is deduced under the assumption that the incident P and SV waves are coherent with each other. When the P and SV waves are not coherent to each other, the general solution is made specific to separate P-wave and SV-wave situations. Critical angles for P and SV excitation are derived. The interface between liquid and solid media is treated next. Both liquid-solid (LS) and solid-liquid (SL) interfaces are separately considered. Several numerical examples are presented to illustrate the critical angle concept.

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