Measurement of Sound Velocity

Phase velocity and attenuation are the real and imaginary parts, respectively, of the complex wave number. Phase velocity can generally be measured more easily and accurately than attenuation. Several theoretical models have been proposed, however, because measurement data are lacking, none of the models can provide a quantitative measure of phase velocity. We describe three models to illustrate the complexity of the problem. 

---

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 /... 

Figure 3.12 Optical diffraction apparatus for measurement of sound velocity (from Hancock and Decius [109]).

This is to be distinguished from the entropy of water in water for which, of course, free-volume values are available directly from measurements of sound velocity. 

Figure235 Block diagram of apparatus for transit-time measurements of sound velocity in pulse-echo mode. (Adapted from Schreiber et al., 1973, reproduced courtesy of McGraw-Hill, New York.)...

Ultrasonic characterization of aqueous solutions of citrates was carried out by performing measurements of sound velocities u(T m) together with densities d(r /w) [160, 171, 172, 174, 178, 181], In these investigations are presented in 5 °C intervals u T-,m) and A T,m) values and they permit to determine the isentro-pic compressibility coefficients Kg(T m) and the apparent molar compressibilities K. (T m) from... 

The value of Warfield and Petree [(1961) I] derived from measurements of sound velocity is too large for cr3rstalline polyethylene by a factor of 3.3. Much of this can be accounted for by the lower heat capacity and expansion coefficient of completely crs talline polyethylene. 

The ratio of the specific heats is therefore determined by (8) from a measurement of the velocity of sound in the gas at a particular temperature, provided the characteristic equation of the fluid is known. 

In the velocity theory above developed it is apparent that while fundamentally sound, the chief difficulty in practice concerns the measurement of bed velocities. This has been overcome in part by Rubey s analysis of the subject, and By the general theory of Kennedy and Lacey. However, in recent years studies of silt movement have utilized DuBoys (1879) expression of tractive force. This expression is simple and convenient and involves the basic elements of channel hydrology depth and slope. Tractive force means the force activity on the bed causing movement of the particulate material. The force required to impart initial motion to the bed material is called the critical tractive force. General movement is defined as the condition where particles up to and including the largest composing the bed are in motion. 

Measurement techniques for determination of sound velocity are given by Kuttruff (1991), Povey (1997b) and Asher (1997). In water, the... 

Saito 7) measured the sound velocity in well-characterized CA solutions with a Pierce type ultrasonic interferometer with high accuracy and determined s. Figure 26 shows the relation between s,, of CA whole polymer solutions and e of the solvent at 25 °C 7). While the dependence of Sq on e differs depending on < F>, s, , except for C A(2.46)-acetone increases with increasing polarity of the solvent in a similar manner as the chemical shifts of the O-acetyl and hydroxyl groups. In Fig. 27, the effects of on Sq for CA-DMAc and CA-dimethylsulfoxide (DMSO) solutions at 25 °C are shown. In both systems, Sq has a maximum at F 2.5 7). 

The adiabatic expansion method is not the best method of determining the heat capacity ratio. Much better methods are based on measurements of the velocity of sound in gases. One such method, described in Part B of this experiment, consists of measuring the wavelength of sound of an accurately known frequency by measuring the distance between nodes in a sonic resonance set up in a Kundt s tube. Methods also exist for determining the heat capacities directly, although the measurements are not easy. 

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,... 

Note that Eq. (6.2.8) may be inverted to determine y from a measurement of the velocity of sound. Inasmuch as y = Cy + R)/Cy, both Cy and Cp are directly available from sound velocity measurements. 

Direct measurement of the velocity or the amplitude of displacement of an imaginary particle submitted to an ultrasonic field is not easy. Filipczynski [132] suggested the use of a capacitance probe method in which the vibrations in the medium are picked up by a diaphragm. The displacement of the diaphragm is measured with an electrostatic microphone, and this is then related to the particle displacement. Sound intensity is given by the relation shown in Eq. (28) where r = particle displacement. The method can be used up to a frequency of 300 kHz. 

The technique itself simply amounts to measuring the sound velocity along a fiber or in a long thin film. This velocity compared with the velocity measured in the same material that is randomly oriented (isotropic) leads to the second moment of the orientation distribution function. 

Bell and Shirley (1980) demonstrated that the P-wave velocity of marine sediments increases almost linearly by about 3 m s per °C while the attenuation is independent of sediment temperature, similar to the temperature dependence of sound velocity and attenuation in sea water. Hence, to correct laboratory P-wave velocity measurements to a reference temperature of 20°C Schultheiss and McPhaiTs (1989) equation... 

In the very high frequency range, Brillouin scattering may be used to measure the sound velocities of aerogels [53]. 

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. 

Analysis of the rotational spectrum of POCI3 in the 18.0—40.0 GHz region gives the following parameters r(P=0) 1.455(5) A, r(P—Cl) 1.989(2) A, and Z.C1PC1103.7(2) , and new values for the isothermal compressibility, specific heat, etc., have been obtained from measurements of the velocity of sound in liquid phosphoryl chloride. 

The refractive index, n, of gaseous fluorine at room temperature has been measured at a number of wavelengths and for medium pressures the results were fitted to the equation — 1 = 20.87 x 10 (1 + 6.4 x 10 A ), where X is the wavelen h of light in microns. Measurements of the velocity of sound in liquid fluorine have been reported for the first time. Data were obtained at 110 and 130 K at pressures up to 21 MN m and should be accurate to within a few percent. Intensity decay of fluorine (F II to F VII) emission lines, between 380 and 1200 A, has been measured and shown to be in good agreement with recent theories. 

An introduction to the general theory of shock tubes is given in Appendix C and in many general references [17-19]. For our purposes, we note that measurement of the velocity of the shock front U permits calculation of the properties of the shocked gas. The Mach number of the unshocked gas, which is the ratio of the shock velocity to the velocity of sound in the unshocked gas, can be written as... 

---