Sound propagation longitudinal mode

It should be remembered here that in cubic crystals, like c-BN, the elastic properties are entirely described in terms of three elastic moduli, Cu, C12 and C44. Cu corresponds to a longitudinal mode propagating along [100], whereas C44 corresponds to a transversal mode propagating in the same direction. C12 is never obtained independently for example, the sound velocity of a transversal mode propagating along [110] is governed by (Cu - Ci2)/2. 

In hexagonal crystals (wurtzite phases of the nitrides, for example), there are five elastic moduli, Cn, C33, C12, C13 and C44. Two of them correspond to longitudinal modes (Cu and C33) along [100] and [001], respectively. C44 may be determined from the sound speed of a transverse mode propagating along [001] C12 appears in combination for example (Cu - Cu)/2 governs one transverse mode in the [100] direction. C13 is present in combination with four other moduli in the velocity of modes propagating in less symmetrical directions, such as [Oil],... 

In our discussion of elastic constants we have imagined uniform distortions of the crystal. An elastic medium can sustain vibrations, which at any instant consist of nonuniform distortions. The normal modes of an elastic continuum arc sound waves (longitudinal and transverse) propagating in the medium, and these normal modes will also exist in the crystal. Indeed, viewing the crystal as an elastic... 

A second mechnism for sound attenuation is mode conversion. The sound waves in air or water are longitudinal waves, where the particle motion is parallel to the direction of sound propagation. With appropriate boundary conditions the longitudinal deformation can be converted to shear deformation or to viscous flow. Conversion to viscous flow is most readily achieved at... 

The SAM is a reflection mode technique that uses a transducer with an acoustic lens to focus the wave below the surface the transducer is scanned acro.ss the sample to create an image [36]. Images from SAM are formed through the interaction of sound waves by direct reflection of the longitudinal waves w ith the sample, or by mode conversion to surface acoustic waves that propagate and scatter. High-resolution images of the material surface... 

Aside from the frequency and sound intensity, the key point in the design of sound-assisted dryers is the mode of energy propagation. Sound energy can be propagated as longitudinal waves (also called compression waves) or transverse waves for which vibration of the particle in the material occurs... 

Associated with each of the two modes of propagation, there is a sound speed and an absorption. Thus, four parameters are required to specify the acoustic properties of a solid isotropic polymer longitudinal speed, shear speed, longitudinal absorption, and shear absorption. 

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