## Treatise on materials science and technology, Volume 3 |

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Page 35

solids (67), however, the use of optical techniques to visualize sound fields in

transparent single crystals has been much more recent (34 ... Figure 12 shows

the ultrasonic beam associated with

axis.

solids (67), however, the use of optical techniques to visualize sound fields in

transparent single crystals has been much more recent (34 ... Figure 12 shows

the ultrasonic beam associated with

**longitudinal wave propagation**along the zaxis.

Page 113

Using this equation of motion they derived expressions for the wave speeds as a

function of the second- and third-order ... He also pointed out that the resonance

interaction of two nonlinear

Using this equation of motion they derived expressions for the wave speeds as a

function of the second- and third-order ... He also pointed out that the resonance

interaction of two nonlinear

**longitudinal waves propagating**in I. THEORY 113.Page 114

the resonance interaction of two nonlinear

same direction leads to the appearance of new longitudinal waves with sum and

difference frequencies relative to the two initial waves. On the other hand, ...

the resonance interaction of two nonlinear

**longitudinal waves propagating**in thesame direction leads to the appearance of new longitudinal waves with sum and

difference frequencies relative to the two initial waves. On the other hand, ...

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Alers aluminum Andreatch anisotropic Appl axis calculated compressive stress copper crystallographic orientation cubic crystals determine direction cosines displacement gradients displacements along 001 elastic moduli elastic wave propagation energy-flux vector equation of motion experimental germanium given by Eq hydrostatic pressure hydrostatic pressure longitudinal hydrostatic pressure transverse ideal orientation interaction isotropic solid linear elastic wave longitudinal wave longitudinal wave propagating materials mode transverse wave nonlinear elastic wave obtain Papadakis particle displacements phonons Phys plane wave pressure longitudinal wave pressure transverse wave pure mode longitudinal pure mode transverse quasitransverse waves rolling direction rolling plane second harmonic second-order elastic constants shear wave single crystals six third-order elastic stress along 001 stress along 110 Substituting Eqs symmetry test specimen texture third-order elastic constants Thurston and Brugger transducer transverse wave ultrasonic beam ultrasonic pulse uniaxial stress values wave along 100 wave normal wave speeds wave velocity Young's modulus