ABSTRACT
In subsequent chapters we shall examine the propagation of ultrasonic waves in an unbounded medium that exhibits only volume elasticity and not elasticity of shape and viscosity, i.e., it is an ideal liquid. According to §I.6, in such a medium, to which we ascribe the properties of an ideal compressible liquid, only elastic hydrostatic compression deformations are possible and, therefore, only one type of elastic wave – a compression (rarefaction) wave – can propagate in it. This considerably simplifies the analysis of perturbations and at the same time enables obtaining the basic acoustic relations for the most common types of waves which can exist in both liquids (and gases) and solids. In solids, as we have seen, other elastic deformations, corresponding to different types of waves which will be examined below, can also exist. However, the relations that we shall obtain for compression waves in an ideal liquid will also be valid for other waves, so that their basic features are common to different types of waves in different media. Real liquids have some elasticity of shape. Such elasticity is significant only at very high deformation rates, greatly exceeding the velocity of ultrasonic waves at the highest frequencies with which they can propagate in the liquid without significant attenuation. This provides justification for considering the deformation rate in an ultrasonic wave to be low enough that the shear elasticity of real liquids can be completely neglected.
