Attenuation of Sound

Abstract

Abstract We will capitalize on our understanding of thermoviscous loss to develop an understanding of the attenuation of sound waves in fluids that are not influenced by proximity to solid surfaces. Such dissipation mechanisms are particularly important at very high frequencies and short distances (for ultrasound) or very low frequencies over geological distances (for infrasound). The Standard Linear Model of viscoelasticity introduced the nondimensional frequency, ωτR, that controlled the medium’s elastic (in-phase) and dissipative (quadrature) responses. Those response curves were “universal” in the sense that causality linked the elastic and dissipative responses through the Kramers-Kronig relations. That relaxation-time perspective is essential for attenuation of sound in media that can be characterized by one or more relaxation times related to those internal degrees of freedom that make their equation of state a function of frequency. Examples of these relaxation-time effects include the rate of collisions between different molecular species in a gas (e.g., nitrogen and water vapor in air), the pressure dependence of ionic association-dissociation of dissolved salts in sea water (e.g., MgSO4 and H3BO3), and evaporation-condensation effects when a fluid is oscillating about equilibrium with its vapor (e.g., fog droplets in air or gas bubbles in liquids).