Acoustic waves II

Abstract

Acoustic impedance, acoustic losses, acoustic waves in piezoelectric solids, and surface waves are discussed in this chapter, along with a number of nonlinear acoustic phenomena. The reflection and transmission of acoustic waves across a boundary is governed by acoustic impedance. One of the most important boundary value problems in acoustics concerns a plane wave incident upon a planar surface, dividing one medium from another. In the general case of an anisotropic medium, the incident beam consists of three waves (one quasilongitudinal, two quasitransverse), each traveling at a different velocity. Each of the three incident waves will be refracted and reflected at the boundary. If the second medium is also anisotropic, each incident wave will generate three reflected waves and three refracted waves, a total of 27 waves in all. Wave propagation in a polycrystalline solid where there are many grain boundaries becomes very complicated. The simpler case of a pure longitudinally-polarized wave at normal incidence to the boundary provides insight into the more general problem. In this case the reflection and transmission coefficients are governed by the relatively simple acoustic impedance parameter (ρc)1/2 = ρv, where ρ is the density, c the stiffness coefficient, and v the phase velocity. The reflection coefficient R at the interface between medium I and medium II is The MKS unit for acoustic impedance is the Rayl (=kg/m2 s). Atypical value for a solid is about 107 rayls. In many acoustic applications it is desirable to reduce reflection by matching the acoustic impedance of the two media. Lithium tantalate transducers are well-matched to iron, for example. Sound transmission from the transducer to the medium can be enhanced with composite materials or with graded coupling layers. Backing materials are often selected to promote reflection. In this case acoustic impedances are mismatched. Tungsten and air are two commonly used backing materials. In an isotropic material the acoustic impedance is (ρc11)1/2 for longitudinal waves and (ρc44)1/2 for shear waves. For anisotropic materials the wave velocities and acoustic impedance change with direction as indicated earlier.