Acoustic Properties

Abstract

When a sound wave passes through a real fluid the intensity of sound decreases with distance traveled. For small pressure amplitudes (and in the absence of cavitation⁽⁴⁹³⁾) it can be assumed that the attenuation (damping) is uniform, such that the intensity I is an exponential function of distance, i.e., $I\left( {x = x} \right) = I\left( {x = 0} \right){e^{ - 2{\alpha _{{a^x}}}}}$, where α _a is the amplitude attenuation coefficient. ^(173,205) The absorption per unit wavelength, μ, is given by the product α _a λ, where λ is the wavelength of sound. For real systems, μ is a function of frequency and in a “well-behaved” system a plot of μ against the frequency of sound wave v has a maximum value μ _max at a particular frequency, the relaxation frequency v _c . The relaxation time $\tau \left[ { = {{\left( {2\pi {\nu _c}} \right)}^{ - 1}}} \right]$ describes the dynamics of response of the system to a pressure perturbation under adiabatic conditions, while μ _max provides information concerning the extent of response. The frequency of the sound wave can, in principle, be varied over a wide range from a few Hz through the audible (v < 14 kHz) to the ultrasonic (14 kHz < v ≲ 800 MHz) and the hypersonic (v > 800 MHz) ranges. However, quite formidable experimental difficulties are encountered in making measurements of sound velocity and sound absorption over the complete frequency range. The majority of sound absorption measurements have been made in the ultrasonic range, 1 ≲ v ≲ 250 MHz. Nevertheless this is an important frequency range because molecular processes having relaxation times in the range 10⁻⁶ ≲ τ ≲ 10⁻⁹ sec can be conveniently probed. Of the more widely used techniques, only dielectric relaxation covers this range, although the conditions governing the coupling between perturbation and system are obviously very different. Before examining some of the acoustic properties of aqueous mixtures some of the underlying theory (see Volume 1, Chapter 12) is briefly outlined.^{(173,205,663)}