Dispersion of sound

Temkin, S., 1966, Attenuation and Dispersion of Sound by Particulate Relaxation Processes, Brown University (available from DDC as AD-630326). (3)... 

An example of dispersion of sound in an air-magnesia mixture with solid-to-air mass ratio, mp, of 0.3 for pp/p (=f) of 100 and 1,000 is illustrated in Fig. 6.10 [Soo, I960]. The figure gives the dispersion of sound for various values of N when the heat transfer is neglected. Under the same experimental condition, the relationship between pag/co and Na, is shown in Fig. 6.11 [Soo, I960]. It is noted that the preceding model is valid only... 

The stress-strain relations for viscoelastic materials are reviewed. The simplest case of intrinsic absorption in polymers is a molecular relaxation mechanism with a single relaxation time. However, the relaxation mechanisms which lead to absorption of sound are usually more complicated, and are characterized by a distribution of relaxation times. Under causal linear response conditions the attenuation and dispersion of sound in a... 

Strictly connected with these ideas are experiments on the absorption and dispersion of sound waves in melanins (370). A resonance absorption was found at 1 MHz, and a rather sophisticated theoretical interpretation allowed correlation of the shear spectrum with the presence of partially ordered structures. Particularly interesting is the observation that hydrated melanins and melanosomes are exceptionally black materials with respect to ultrasound absorption. 

Acoustic absorbance and insulation are accomplished by dispersion of sound waves in the open cells. 

Kono R, Yamaoka H, McGinness J (1979) Anomalous AbsOTption and Dispersion of Sound Wave in Diethylamine Melanin. J App Phys 50 1242... 

Fig. 13. The dispersion of sound in neon. Here Vo is the ideal gas sound speed and f the dimensionless frequency f = (3ri/5nokaT)]...

We used the concept of sound velocity dispersion for explanation of the shift of pulse energy spectrum maximum, transmitted through the medium, and correlation of the shift value with function of medium heterogeneity. This approach gives the possibility of mathematical simulation of the influence of both medium parameters and ultrasonic field parameters on the nature of acoustic waves propagation in a given medium. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

For general aspects on sonochemistry the reader is referred to references [174,180], and for cavitation to references [175,186]. Cordemans [187] has briefly reviewed the use of (ultra)sound in the chemical industry. Typical applications include thermally induced polymer cross-linking, dispersion of Ti02 pigments in paints, and stabilisation of emulsions. High power ultrasonic waves allow rapid in situ copolymerisation and compatibilisation of immiscible polymer melt blends. Roberts [170] has reviewed high-intensity ultrasonics, cavitation and relevant parameters (frequency, intensity,... 

Kieffer has estimated the heat capacity of a large number of minerals from readily available data [8], The model, which may be used for many kinds of materials, consists of three parts. There are three acoustic branches whose maximum cut-off frequencies are determined from speed of sound data or from elastic constants. The corresponding heat capacity contributions are calculated using a modified Debye model where dispersion is taken into account. High-frequency optic modes are determined from specific localized internal vibrations (Si-O, C-0 and O-H stretches in different groups of atoms) as observed by IR and Raman spectroscopy. The heat capacity contributions are here calculated using the Einstein model. The remaining modes are ascribed to an optic continuum, where the density of states is constant in an interval from vl to vp and where the frequency limits Vy and Vp are estimated from Raman and IR spectra. 

As pointed out by Hayward (96) equation (17) cannot be used uncritically. In the presence of adsorption (which is known to occur for MgSO solutions) (97-104) the velocity of sound (u0) is shifted and becomes a complex function (105). The shift or dispersion, in velocity (Au) caused by relaxation can be estimated from (105)... 

The motion of atoms in the lattice can be depicted as a wave propagation (phonon). By dispersion we mean the variation in the wave frequency as reciprocal space is traversed. The propagation of sound waves is similar to the translation of all atoms of the unit cell in the same direction hence the set of translational modes is commonly defined as an acoustic branch. The remaining vibrational modes are defined as optical branches, because they are capable of interaction with light (see McMillan, 1985, and Tossell and Vaughan, 1992, for more exhaustive explanations). 

Particle mobility and zeta potential can now be measured by more sophisticated techniques. With photoelectrophoresis, particle mobility is measured as a function of pH under the influence of ultraviolet radiation. At pH < 8, the electrophoretic mobility of irradiated hematite particles (A = 520 nm) was markedly different from that measured in the absence of UV irradiation. This was attributed to the development of a positive surface charge induced by photo-oxidation of the surface Fe-OH° sites to (Fe-OH) sites (Zhang et al., 1993). The electroacoustic technique involves generation of sound waves by the particles in the colloidal dispersion and from this data. 

To answer the above question new results have been obtained by the study of very fast protolytic reactions in aqueous solution. These were carried out during the last few years by means of relaxation methods (sound absorption, dispersion of the dissociation field effect, temperature jump method) (for a survey cf. [3]). The neutralization reaction HgO+ -j- OH- - (Ha0)8 is the most characteristic example. It was possible to determine the rate constant of this reaction by measuring the time dependence of the dissociation field effect of very pure water of specific conductivity of 6 7 10-8 (at 25°C). 

Einstein showed that when a reversible reaction is present sound dispersion occurs at low frequency the equilibrium is shifted within the time of oscillation, the effective specific heat is at a maximum, and the speed of sound c0 is at a minimum. At high frequency the oscillations occur so rapidly that the equilibrium has no time to shift (it is frozen ). The corresponding Hugoniot adiabate (FHA) is shown in the figure. Here the effective heat capacity is minimal, the speed of sound c is maximal cx > c0. From consideration of the final state and the theory of shock waves it follows that C>c0. 

For a monatomic gas, where the heat capacity involves only translational energy, V is independent of sound oscillation frequency (except at ultra-high frequencies, where a classical visco-thermal dispersion sets in). For a relaxing polyatomic gas this is no longer so. At sound frequencies, where the period of the oscillation becomes comparable with the relaxation time for one of the forms of internal energy, the internal temperature lags behind the translational temperature throughout the compression-rarefaction cycle, and the effective values of CT and V in equation (3) become frequency dependent. This phenomenon occurs at medium ultrasonic frequencies, and is known as ultrasonic dispersion. It is accompanied by... 

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