Mean sound velocity

Debye temperature are obtained from elastic data using the mean sound velocity and mean atomic volume in the relation... 

But the rolls are made from cast iron and that means that the sound velocity is not constant on the entire roll. 

As long as the Mach number is small—meaning the velocities are small compared to the sound speed—it is reasonable to assume that the incompressible continuity equation is a good approximation for isothermal, single-species flow. That is, velocity variations have little effect on density variations. As a result the simplifications associated with V-V 0 can be enjoyed. In practical terms, most consider that flows with Ma < 0.3 can be assumed to be gas-dynamically incompressible. 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The chemical effects of ultrasound do not arise from a direct interaction with molecular species. Ultrasound spans the frequencies of roughly 15 kHz to 1 GHz. With sound velocities in liquids typically about 1500 m/s, acoustic wavelengths range from roughly 10 to 10 4 cm. These are not molecular dimensions. Consequently, no direct coupling of the acoustic field with chemical species on a molecular level can account for sonochemistry or sonoluminescence. Instead, sonochemistry and sonoluminescence derive principally from acoustic cavitation, which serves as an effective means of concentrating the diffuse energy of sound. 

For practical purposes it is necessary to represent the connection between the ultrasonic sound velocity u (m/sec) and v, n and d by means of cross-sections for constant log v values of the log v -n-d space model. The sections contain the intersecting lines with the surfaces of equal u values, Figs. 30, 31, 32, 33 and 34. 

It is also possible to determine the surface tension of hydrogenated fractions from the ultrasonic sound velocity and the density22. This can be done by means of a u-d diagram in which lines of equal values of the surface tension have been constructed. This diagram is shown in Fig. 46. 

Measurements of sound velocity at ultrasonic frequencies are usually made by an acoustic interferometer. An example of this apparatus11 is shown in Fig. 2. An optically flat piezo-quartz crystal is set into oscillation by an appropriate electrical circuit, which is coupled to an accurate means of measuring electrical power consumption. A reflector, consisting of a bronze piston with an optically flat head parallel to the oscillating face of the quartz, is moved slowly towards or away from the quartz by a micrometer screw. The electrical power consumption shows successive fluctuations as the distance between quartz and reflector varies between positions of resonance and non-resonance of the gas column. Measurement of the distance between resonance positions gives a value for A/2, and if /... 

Acoustical temperature sensors can theoretically measure temperature from the cryogenic range to plasma levels. Their accuracy can approach that of primary standards. Temperature measurements can be made not only in gases but also in liquids or solids, on the basis of the relationship between the sound velocity and temperature shown in Figure 3.163. The acoustic velocity can be detected by immersing a rod or wire into the fluid or by using the medium itself as an acoustic conductor. The sensor rod can measure the temperature at a point or, by means of a series of constrictions or indents, can profile or average the temperature within the medium. 

The mechanical properties of polymers are controlled by the elastic parameters the three moduli and the Poisson ratio these four parameters are theoretically interrelated. If two of them are known, the other two can be calculated. The moduli are also related to the different sound velocities. Since the latter are again correlated with additive molar functions (the molar elastic wave velocity functions, to be treated in Chap. 14), the elastic part of the mechanical properties can be estimated or predicted by means of the additive group contribution technique. 

Our conclusion is that by means of four additive molar functions (M, V, UR and Uh) all modes of dynamic sound velocities and the four dynamic elastic parameters (K, G, E and) can be estimated, c.q. predicted from the chemical structure of the polymer, including cross-linked polymers. 

Example Gas Temperature Calculation by Use oj Sound Velocities. What is the air temperature if the sound velocity through it is 1.53 X 10 cm./sec. By means of Eq. (13), one can calculate the translational temperature of a gas from the measured velocity of sound transmitted through it. However, this relationship also contains the temperature-dependent variables y and M, so it is not possible to calculate the temperature explicitly from the sound velocity. In Fig. 4, the... 

The mean molecular velocity is given by (SRT/irM), while the velocity of sound is given by (yRT/M), both increasing as T. The velocity also increases because of the increase in space velocity due to the heating. 

Passynski measured the compressibility of solvent (fig) and solution (fi), respectively, by means of sound velocity measurements. The compressible volume of the solution is Vand the incompressible part, v (v/V = a). The compressibility is defined in terms of the derivative of the volume with respect to the pressure, P, at constant temperature, T. Then,... 

This means that in the elastic region, pressure and density are linearly related. Beyond the elastic region, the wave velocity increases with pressure or density and Pip is not linearly proportional. Wave velocity continues to increase with stress or pressure throughout the region of interest. Therefore, up to the elastic limit, the sound velocity in a material is constant. Beyond the elastic limit, the velocity increases with increasing pressure. Let us look at a major implication of this fact. Consider the pressure wave shown in Figure 14.3. 

The sound velocity in a fiber, and the sonic modulus calculated therefrom, are related to molecular orientation (De Vries ). As shown by Moseley ), the sonic modulus is independent of the crystallinity at temperatures well below the T (which means that the inter- and intramolecular force constants controlling fiber stiffness are not measurably different for crystalline and amorphous regions at these temperatures). An orientation parameter a, calculated from the sonic modulus, is therefore taken as a measure for the average orientation of all molecules in the sample, regardless of the degree of crystallinity. The parameter is called the total orientation , as contrasted to crystalline and amorphous orientation, from X-ray data. 

Specificity is the most important requirement in gas analysis. Techniques dependent on the physical properties of the gas molecules, such as thermal conductivity, density, viscosity, and sound velocity, generally have insufficient specificity to differentiate a single gas in a mixture of gases, and therefore must incorporate in the procedure some type of preliminary separation. Vapor phase fractionation (gas chromatography) is an example of a popular analytical technique based upon a physical property (thermal conductivity) of the gas that requires preliminary separation of the gases by means of special columns (molecular sieve, silica gel, etc.). 

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 British standards BS 2782, Methods 620 A-D [6]. are identical to ISO 1183. ASTM D 792 [7] covers the displacement method and has two procedures, one for the displacement of water and one for that of other liquids. It is not clear why it has been split in this way, and it is notable that there is no mention of using a sinker, nor does it include a pycnometer method. The density gradient method is given in ASTM D 1505 [8] and is very similar to the ISO procedure. There is also an ASTM method for density of polyethylene by means of ultrasound, ASTM D 4883 (9). This works on the principle of measuring sound velocity in the plastic, which correlates to density. The apparatus requires calibrating with reference materials but is claimed to give accuracies of 0.08% or better. The use of the method would mostly be in quality control, and it is questionable whether it should have been standardized. Essentially it describes the use of a commercial in.strumcnt with no apparatus details, not even the frequency used. 

When p and (dp[Bp)T are known, the measurement of W provides a means for obtaining valuable information on thermodynamic properties which are accessible to direct measurement only with difficulty. For a liquid system ir equilibrium w ith its vapor, properties are mostly measured as a function of both temperature and pressure. As the propagation of sound is an adiabatic process, data on the sound velocity make it possible to solve this simultaneous dependence and to distinguish the separate contributions of p and T in the change of thermodynamic properties. 

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