The speed of sound c_s is therefore:

Equation (3.13) also indicates how the speed of sound in liquids can be measured; this is discussed in greater detail in Section 4.4.1.

The basic idea of ultrasonic spectroscopy is to obtain information about the medium by measuring how the sound field changes between transmitter and receiver. Absorption provides an indicator of this change: energy is removed from the sound wave according to

Here α(ω) is the sound attenuation coefficient employed in ultrasonic absorption spectroscopy. The acoustic energy E(x) is not the most convenient quantity for extracting information about the medium. The sound pressure p(x), which is proportional to the square root of the energy, is better suited:

The following sections examine the properties of the attenuation coefficient as a carrier of information about the liquids investigated.

3.1.1 Sound Absorption in Liquids

Equation (3.15) is not merely a trivial assumption about pressure. Rather, it is a solution of the wave equation with losses, derived from continuum mechanics [20]. However, it does not specify the nature of those losses or the molecular processes occurring in the liquid. For that purpose the absorption coefficient α(ω) must be examined more closely.

3.1.1.1 Classical Attenuation

1. Viscous attenuation. Even an idealized fluid whose molecules are modeled as hard spheres exhibits a mechanism for sound absorption. Molecules set in motion by the sound wave transfer part of their momentum to neighboring molecules, thereby losing some of their kinetic energy through internal friction.