Velocity of sound

The time of flight is measured and because of the fixed distanee of the transducers the actual sound velocity of... 

Of our special interest is the thickness measurement of powder coatings. While the sound velocity of the electrostatic applied powder/air mixture is estimated to be two times the velocity in air it is also an estimation that thickness powder / air layer is reduced by a factor of 5 by smelting (burning in process, hardening). 

In this chapter we define what is meant by a shock-wave equation of state, and how it is related to other types of equations of state. We also discuss the properties of shock-compressed matter on a microscopic scale, as well as discuss how shock-wave properties are measured. Shock data for standard materials are presented. The effects of phase changes are discussed, the measurements of shock temperatures, and sound velocities of shock materials are also described. We also describe the application of shock-compression data for porous media. 

Assuming the pressure pulse travels with the sound velocity of the mud, how long will it take to reach the rig floor in a 12,000-ft borehole The sound velocity in the mud is given by... 

High-Pressure Research, 23, 229 (2003). Measured Sound Velocities of H20 and CH3OH. 

For some homogeneous explosives detonation performance is strongly influenced by the density and sound velocity of the charge casing. 

As has been stated above the lines for equal values of the ultrasonic sound velocity of mineral oil fractions in the log v -(n — d) graph are straight. Therefore it is possible to construct a nomogram with the parallel coordinates log v% and (n — 0.181 d), the value of 0.181 in the function (n — 0.181 d) being somewhat more accurate than in the function (n — d). 

The sound velocity, c0, of single crystal RDX is quoted in Ref 84 as 2,55km/sec. Extrapolation of Hugoniot data (see below) gives c0 = 2.87km/sec for RDX at 1,8g/cc (Ref 34). The writer (Ref 37) found that sound velocity of pressed RDX pellets varies with packing d, particle size, and temp as follows ... 

From Eq. (11), an obviously desirable characteristic for thermoelectric materials is to have low thermal conductivity k. The thermal diffusivity constant, Dt, of ErB44Si2 has been found to have small values of Dt < 1.1 x 10 2 cm 2/s (Mori, 2006c). These values are significantly smaller than what has been observed for boron carbide samples (Wood et ah, 1985). Although no data exists for the sound velocities of ErB44Si2, the velocities are probably high since borides are typically hard materials. Therefore, the small values of Dt indicate extremely short phonon... 

Figure 2.20. Right part The polariton dispersion at a few tens of reciprocal centimeters below the bottom of the excitonic band, vs the wave vector, or the refractive index n = ck/w (notice the logarithmic scale). The arrows indicate transitions with creation of one acoustical phonon, with linear dispersion in k (with a sound velocity of 2000 m/s). For the transitions T, Tt, T3 the final momentum is negligible compared to the initial momentum, and the unidimensional picture suffices. For the transitions between T3 and the point A, the direction of the final wave vectors should be taken into account. Left part The density of states m( ) (2.141) of the polaritons in the same energy region. This diagram explains why the transitions T, will be much slower than the transitions around T3 and the point A. The very rapid increase of m( ) at a few reciprocal centimeters below E0 shows the effect of the thermal barrier.

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. 

FIG. 14.6 Cubic root of longitudinal sound velocity of polyethylene as a function of density. 

Fiquet G., Badro J., Guyot F., Requardt H., and Krisch M. (2001) Sound velocities of iron to 110 gigapascals. Science 291,468-471. 

The results obtained for lead azide are summarized in Table IX and in Figure 30. The highest temperature achieved at the aluminum-lead azide interface was less than 120°C, which is significantly below the lowest value (297°C) for the thermal initiation of lead azide. The data indicated a stress initiation threshold of 3.6 kbar for the lead azide, assuming a sound velocity of 2.5 km/sec for the explosive. The stress pulse-width was approximately 0.2 psec. If the wave velocity (shock velocity) of 1.23 km/sec is assumed for dextrinated lead azide, then a lower bound of 2.2 kbar can be placed on the threshold for RD1333 lead azide. 

Final temperature due to energy deposition neglecting thermal losses. Assuming sound velocity of 0.2 5 kiii usec for RD1333 lead azide. Measured stress in quartz. 

The results of this calculation are given in Fig. 8. We see that the wave vector has a mean value of 2.41 10 cm and changes within values of 2.34 10 cm to 2.5 10 cm" (+,- 3.5%). We see that it can have a linear effect in the sound velocity determination but a quadratic effect in sound absorption. From here, we calculate the sound velocity for all temperatures as shown in Fig. 9. The Fig. 9 provides data for the temperature dependence of the sound velocity once corrected by the refraction effects. There we see that the sound velocity of the lower phase smoothly decreases with temperature within the two-phase region, whereas that for the upper phase shows a stronger trend. In a previous work and in a different phase transition, K. V. Kovalenko et al. ... 

The sound velocity of pure methanol (CH3OH) and pure ethanol (C2H5OH) was measured along a 250° C isotherm up to 3.9 GPa. After each data point was taken the sample was cooled and the velocity was again measured and compared to previous measurements of uncooked methanol. No appreciable velocity difference between data sets was observed. 

We have measured sound velocities of various supercritical fluid systems. An attempt to carry forward such measurements on higher temperature isotherms of formic acid was frustrated by chemical reaction toward products that may include carbon dioxide, carbon monoxide, water, hydrogen and differentiated solid-like products at even higher temperatures and pressures. Nonetheless, the diamond anvil cell provides a unique opportunity to study the chemistry and kinetics of fluids under extreme conditions. We also find that CH2O2 is present during the detonation of some common explosives. 

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