Sound longitudinal velocity

L being the longitudinal velocity of sound in the crystal and a the lattice spacing. lc will be found useful in establishing a distance dependence of the resonance mode, to which we turn now. 

The dispersion relation of phonons traveling in chain direction shows a large difference between the slopes of the longitudinal and the transverse branches which points to a clear distinction in the strength of intra- and interchain forces. This is confirmed by the upward curvature of the lower transverse branch and by a comparison of the longitudinal velocities of sound for different crystallographic directions. 

The solid curves in Fig. 8.37 were computed with only one free parameter in Eq. (8.67), namely the longitudinal velocity of sound = 4 10 cm/s. /xq is not a fit parameter, since the zero-field mobility follows directly from the measurable slope of vd(F) for F 0 (see Fig. 8.37). The value for ce obtained in this way agrees surprisingly well with the independently-measured longitudinal sound velocity (compare Table 5.4) and is thus a good indication that the Shockley model for the electron-phonon coupling is also applicable to organic molecular crystals. 

The velocity of sound longitudinal waves in a medium, denoted and expressed in m.s , is given by the following equations ... 

Longitudinal velocity of sound (VJm.s ) Transversal velocity of sound (V m.s )... 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

If we accept the assumption that the elastic wave can be treated to good aproximation as a mathematical discontinuity, then the stress decay at the elastic wave front is given by (A. 15) and (A. 16) in terms of the material-dependent and amplitude-dependent wave speeds c, (the isentropic longitudinal elastic sound speed), U (the finite-amplitude elastic shock velocity), and Cfi [(A.9)]. In general, all three wave velocities are different. We know, for example, that... 

The best of all methods of measuring E is to measure the velocity of sound in the material. The velocity of longitudinal waves, v, depends on Young s modulus and the density, p ... 

Even better agreement is observed between calorimetric and elastic Debye temperatures. The Debye temperature is based on a continuum model for long wavelengths, and hence the discrete nature of the atoms is neglected. The wave velocity is constant and the Debye temperature can be expressed through the average speed of sound in longitudinal and transverse directions (parallel and normal to the wave vector). Calorimetric and elastic Debye temperatures are compared in Table 8.3 for some selected elements and compounds. 

Designations 1 2=Constants 3 = Longitudinal sound velocity 4 =Detonation velocity 5 = Chapman-Jouguet pressure 6 =... 

The material for an acoustic lens should have a low attenuation, and a high velocity to minimize aberrations. Sapphire is an excellent material in both these respects. But the high velocity has a less desirable consequence. An acoustic impedance can be defined, which is equal to the product of the velocity and the density. The impedance of sapphire for longitudinal waves travelling parallel to the c-axis is thus 44.3 Mrayl, compared with the impedance of water which at room temperature is about 1.5 Mrayl, rising to 1.525 Mrayl at 60°C. When sound is transmitted across an interface between two materials of different impedance, the stress amplitude transmission coefficient is ( 6.4.1 Auld 1973 Brekhovskikh and Godin 1990)... 

Sound Velocity Through Explosive. Longitudinal and transverse shear sound velocities were... 

Longitudinal Sound Velocities and Hugoniot Data U = shock vel u = narticle vel co — Innei-... 

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