ABSTRACT
In formulating the equations describing the propagation of sound in an ideal fluid we assumed that local thermodynamic equilibrium was achieved instantaneously in the fluid. The local temperature and pressure were assumed to follow the local density along an isentropic path. However, we have already seen that diffusion of heat and momentum causes the thermodynamic path of the acoustic cycle to deviate from an isentropic one. Often, there are other relaxation mechanisms operating in the fluid which give rise to a delay between the imposition of a density change and the establishment of the equilibrium temperature and pressure. We will show that if the relaxation times characterizing these mechanisms are short compared with 1/ω then the internal friction of bulk viscosity results with η b real and independent of frequency. When this term is included, the hydrodynamic equations can be applied with confidence. However, if the delay in the attainment of local equilibrium is of the order of 1/ω then large effects can result that are not adequately described by the theory so far derived.
