Absorption of sound

The time constant r, appearing in the simplest frequency equation for the velocity and absorption of sound, is related to the transition probabilities for vibrational exchanges by 1/r = Pe — Pd, where Pe is the probability of collisional excitation, and Pd is the probability of collisional de-excitation per molecule per second. Dividing Pd by the number of collisions which one molecule undergoes per second gives the transition probability per collision P, given by Equation 4 or 5. The reciprocal of this quantity is the number of collisions Z required to de-excite a quantum of vibrational energy e = hv. This number can be explicitly calculated from Equation 4 since Z = 1/P, and it can be experimentally derived from the measured relaxation times. 

Perturbation of a spin-state equilibrium by ultrasound results in the absorption of sound, the absorption coefficient a (neper cm ) being determined as a function of frequency /(Hz) according to ... 

S. A. Al tshuler, Resonant absorption of sound in paramagnetic materials, Dokl. AN SSSR, 1952, 85, 1235. 

These are two extremes. An intermediate situation, where the period of the sound wave is comparable to the relaxation time, occurs when reaction is fast enough to allow the concentrations to alter with time, but the change in concentration is out of phase with the sound wave. This shows up as an increase in the velocity of sound, or as a maximum in the absorption of sound by the reaction mixture as the frequency of the sound wave alters. This is the region where all the useful information is obtained. 

K. Herzfeld, in Dispersion and Absorption of Sound by Molecular Processes, edited by D. Sette, Academic, New York, 1963, p. 272 ff. 

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... 

The most widely used materials for absorption of sound are viscoelastic polymers, and these material are discussed in a separate section. 

Absorption, definition, 168 Absorption of sound in viscoelastic materials. See Sound absorption in viscoelastic materials Acoustic, definition, 25-26... 

A sound wave is passed through an electrolyte solution in which there are species present at equilibrium. This is done over a range of frequencies of the sound wave, and the absorption of sound energy by the solution, or the velocity of the sound wave is measured for each frequency. The sound wave is equivalent to a pressure wave or to a series of alternating temperatures, and these call for a corresponding wave of new equilibrium positions to be set up. 

If, however, the concentrations can alter rapidly enough, and the new equilibrium positions can be set up but are out of phase with the periodic displacement of the soimd wave, then this shows up as an increase in the velocity of the sound wave, or as a dramatic increase in the absorption of sound (see Figure 1.2(a) and (b)). Each time this happens an equilibrium process is adjusting itself. The number of times this happens shows directly the number of equilibrium processes occurring in the solution which are being disturbed by the sound wave (see Figure 1.2(c) and 1.2(d)). Sometimes two or more peaks are superimposed, but these can be resolved by standard curve-fitting techniques. 

However, there still remains the fundamental problem of identifying the process chemically. Identification of the process in the chemical sense is ambiguous as there is no direct chemical observation of the system. It is easy to distinguish between chemical processes and physical processes, such as ion-solvent interactions or energy transfer, by the frequencies at which the maxima in the absorption of sound occurs. Identification of the chemical equilibria and the chemical species present are inferred through a fit of theory plus inference with experiment, and the data may be susceptible to more than one interpretation. One clue which has been used is that the frequency at which absorption of... 

Two maxima mean two equilibria to be identified. A is ruled out because diffusion is unlikely to give absorption of sound at the frequencies involved. 

Ultrasonic sound waves propagating in a liquid solution create repetitive pressure/density variations. Some versions measure the absorption of sound energy and others involve the scattering of a light beam. They are useful for very fast reactions, but each instrument tends to be limited to a small time range. Although operation at high pressures is possible, such an application would be very specialized. 

Jungle Eglin, AFB Aug 02 Scattering absorption of sound due to dense vegetation. 

A classical problem in acoustics is the absorption of sound in solid suspensions. Sewell (1910) first conducted a theoretical study of the case of small rigid spherical particles suspended in fluids. The condition of immobility in this case is satisfied by water droplets in air thus, Sewell s treatment can be applied to sound propagation in fogs and clouds. 

Schneider (266, 267) has studied the conduction of sound of 600-kc frequency in the neighborhood of the critical temperature. As the temperature rises the velocity of sound in both liquid and gas decreases up to the critical temperature. At the critical temperature and pressure the velocity is 121.5 meter/sec. Above this temperature the velocity increases. There is a very sharp maximum in the absorption of sound over a range of about 1° with the peak at the critical temperature. From these data the heat capacity at constant volume, near the critical temperature, has been calculated (268). 

When ultrasonic pulses (10 kHz-300 MHz) pass through a liquid containing a solute involved in a two-state equilibrium, anomalies in the absorption of sound energy are observed at certain frequencies due to interaction with the exchanging system. Such effects are only observed when the equilibrium is biased 1), and they are observed even when less than 1% of the minor component is present (Davies and Lamb, 1957). 

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