On the Theory of the Propagation of Plane, Finite Amplitude Waves in a Dissipative Fluid

Abstract

The dissipationless theory for harmonic generation in an initially sinusoidal, plane, finite-amplitude wave is used as a basis for calculation of the harmonic components of such a wave in a fluid with dissipation.The assumption used is shown to lead approximately to the relationships of the Fox and Wallace theory. The result is given as a Fourier series, with graphs of the first few harmonic components for two specific cases. The series representation is valid for distances X_< L, where L is the discontinuity distance for the dissipationless case. NOTATION C'-Velocity of wave phase points. Co-Sound velocity for infinitesimal amplitudes. P-Pressure. P0-Internal (equilibrium) pressure. p-Density. p0-Equilibrium density. .. A, B-Empirical constants in the equation of state. X= Distance from origin of wave. U-Particle velocity. a--Infinitesimal amplitude absorption coefficient for the fundamental frequency component. f(n)=Factor by which a must be multiplied in order to obtain the absorption coefficient of the nth harmonic in the medium of interest. v= Fundamental frequency. L-Discontinuity distance for dissipationless case. K-X/L= Reduced distance. r= ox/r. P, (K) --Pressure amplitude of the nth harmonic wave component, measured at reduced distance K. /•(•)--Harmonic generation parameter (Fox and Wallace).

Laser Pulses and the Generation of Acoustic Transients in Biological Material

“…The steepening of the wave front results in the production of higher-frequency components. The generation of high-frequency harmonics has been described by Lester (1961) as a function of propagation distance. For large-amplitude waves, the equation of state of the liquid is assumed to be of the form (29) where A and B are empirical constants and P and Po are the pressures at fluid densities p and Po, respectively.…”