Dispersion Of Sound Velocity Research Articles

Interdependence of Spectral Line Breadth, Sound Velocity Dispersion, and Viscosity of Small Molecules in the Gas Phase

An examination of the data on bimolecular collisions of small molecules has produced several new insights and predictions. The data on viscosity, sound velocity dispersion, and spectral line breadths in the microwave, infrared, and Raman regions have been assembled for H2, O2, N2, CH3Cl, and HCN. These data have been put on an equivalent basis of calculated or observed spectral line breadth constants. When this is done, the relative importance of elastic and inelastic rotational collisions may be assessed. The data on H2 are here used to predict a collisional narrowing of the ordinary Doppler linewidth; this narrowing effect can be found in the literature, where the significance of the extremely narrow lines has not been fully appreciated. The line breadths observed in the microwave spectrum of oxygen are seen to be peculiar to some phenomenon which reorients electron spins but does not alter rotational states. Spin exchange is here identified as the most probably mechanism for microwave line broadening in O2. The differences between isotropic and anisotropic linewidths in the Raman spectra of H2, O2, and N2 indicate that a thorough theoretical treatment of Raman linewidths is required. Some additional experiments on line breadths in the Raman spectra of H2, O2, and N2 are suggested. The basic approximation in Anderson's impact theory for broadening of spectral absorption and emission lines is seen to be quantitatively invalid for self-broadening of these homonuclear diatomic molecules. This is the approximation of classical (straight) paths. Two new phenomena are predicted for the propagation of rotational energy in small polar molecules. The first of these is a separation of the rotational sound velocity dispersion into two regions for symmetrictop molecules. The region of lower frequency dispersion should account for R/2 of heat capacity, and be associated with changes in rotation about the unique axis of the molecule. Small polar molecules with large dipoles (particularly the alkali halide vapors) should also exhibit a peculiar form of energy propagation in the rotational degrees of freedom only. This ``roton propagation'' may also influence the behavior of shock waves in polar gases and the heat conductivity at very low pressures.

Hypersonic Velocity in Viscous Liquids as revealed from Brillouin Spectra

Taking into consideration Lamb's theory for the propagation of high frequency acoustical waves in viscous liquids, and the idea of Maxwell regarding complex viscosity, a theoretical expression has been deduced for the velocity of high frequency acoustical waves through viscous liquids. It is observed that if Frenkel's expression for the rigidity modulus of a liquid be introduced into the formula for wave propagation then the theoretical formula explains the dispersion of sound velocity in viscous liquids as was observed by Venketeswaran from Brillouin spectra and the theoretical value is in good agreement with the experimental result. Further, the introduction of complex viscosity partly explains the propagation of these high frequency waves through viscous liquids.

Dispersion and Absorption of Sound in Ethyl Formate and Study of the Rotational Isomers

It was shown by Karpovich that there is the relaxational absorption of sound in liquid ethyl formate and that it results from the rotational isomerism about the C–O bond. Dispersion of sound velocity is expected from the absorption data, and its existence is confirmed by the present experiments. The sound velocities are measured over the frequency range from 300 kc to 9 mc/sec and at 5°C intervals from 10°C to 40°C by an ultrasonic interferometer. From these experimental results, the energy differences, the equilibrium constant, the rate of isomerization, and the height of the potential barrier hindering the internal rotation are calculated. The value of the energy difference is 2.50 kcal/mole and the height of the potential barrier, referred to the higher energy state is 3.38 kcal/mole. The calculated values of the heat capacity owing to the chemical reaction, the sound velocity at infinite frequency, and the maximum values of the absorption coefficient of sound per wavelength are in good coincidence with the experimental data.

A Liquid with Unusually High Sound Velocity

During a study of the effect of molecular structure on sound velocity in liquids, a liquid was found in which the velocity of sound is 3000 meters/second at 20°C, as measured by a 3-Mc ultrasonic interferometer. Previously the highest value known was less than 2000 meters/second, for glycerine. The new liquid is a viscous concentrated aqueous solution of sorbitol, prepared by heat dehydration of the commercial syrup “Arlex.” Sorbitol was selected for study, even though it is a solid, because its chemical structure is that of a double glycerine molecule. Concentrated sorbitol solutions also show a dispersion of sound velocity with frequency in the megacycle range (reminiscent of the behavior of polyisobutylene as described by Mason) and absorption coefficients many times larger than that of glycerine.

Dispersion of sound velocity in some alcohols

Adiabatic compressibility of six alcohols at different temperatures have been determined by a modified form of Tyrer’s piezometer. The densities of the liquids at different temperature have been found by a specially designed pyknometer. From these data the theoretical acoustic velocity at sonic frequency has been calculated from the relation\(v = 1/\sqrt {\beta _\phi \rho } \). Using the same sample of the alcohols, the ultrasonic velocities are determined for different temperatures at a frequency of about 2000 KC/sec. In all these measurements special precautions have been taken to keep the temperature constant. The magnitude of dispersion is shown by drawing the velocity temperature graphs for both frequencies. It is found that there is evidence of dispersion in all the alcohols except perhapsn-propyl alcohol. Inn-butyl alcohol the ultrasonic velocity is lower than the sonic, while in all the other cases, the ultrasonics are higher.

On the Thermal Conductivity of Dielectrics

As is well known, Peierls and Debye found that, if $T\ensuremath{\gg}\ensuremath{\theta}$ ($T$ is the temperature, $\ensuremath{\theta}$-the Debye temperature), the thermal conductivity $\ensuremath{\kappa}$ of dielectrics varies inversely to the temperature. However, this turns out to be true only for dielectrics obeying the definite law of sound velocity dispersion and the definite law of the dependence of sound velocity on the direction. For all other dielectrics at $T\ensuremath{\gg}\ensuremath{\theta}$, $\ensuremath{\kappa}$ is inversely proportional to ${T}^{\frac{3}{2}}$. This results from investigation of the free path of long elastic waves.

Dispersion of Sound Velocity in Liquids

As is now well known1, the spectral character of monochromatic light scattered by many liquids exhibits an observable change as the result of such scattering; an instrument of sufficiently high resolving power, for example, a Fabry-Perot etalon2, indicates the presence of Doppler-shifted components on either side of the main radiation. From this we are able to infer that sound waves of very high frequency represent a considerable part of the energy of thermal agitation in such liquids. The frequency of the sound-waves actually revealed by this method depends on the wave-length of the incident light, the angle of scattering and the liquid employed; in most actual cases, it lies within the frequency range 1,000–10,000 megacycles per second.