Absorption of the wave energy results in its degradation to heat. This occurs when the density fluctuations in the medium get out of phase with the sound pressure fluctuations. In 'homogeneous' media (e.g. solutions of macromolecules) the mechanisms by which this is known to occur are relaxation mechanisms. These are not fully understood even in very simple media but arise from the time-lag that is inherent in the perturbation of any physical or chemical equilibrium initiated by the cyclic fluctuations of the wave parameters. At any instant in time the total wave energy may be viewed as being shared amongst a number of different forms of energy: translational energy, molecular vibrational and structural energy, and lattice vibrational and structural states. As time varies, redistribution of the energy occurs, but at finite rates determined by the precise coupling processes relevant to the propagation medium. The coupling processes themselves constitute the absorption mechanisms, the type and number of which may vary enormously from liquid to liquid.
A general form for the equation describing the absorption at a frequency f (wavelength l) due to a single process of this kind is or=_6__(4ii)
f2 1+(f/fR)2 j where A = 2[(aRl)max/cfR] is a constant (sometimes called the relaxation amplitude) defined by the maximum value of the wavelength-absorption or absorption per cycle1 (al), the speed (c) and the relaxation frequency (fR). Figure 4.1a helps to visualise the form of this equation.
At low frequencies the wave parameters fluctuate slowly enough for the redistribution of energy nearly to 'keep up', energy is returned to the wave from its other shared forms only slightly out of phase, and the absorption is low. As the frequency increases, energy is returned more out of phase and the absorption increases until, at frequencies much higher than the relaxation frequency, the wave does not have time fully to perturb the equilibrium of the medium and there is little sharing of the wave energy from its purely translational form. The wavelength-absorption reaches a maximum value when f=fR.
In an attempt to describe observed absorption versus frequency curves a number of such processes are considered, summed and added to the so-called 'classical absorption coefficient' (as calculated by Stokes and Kirchoff over a century ago). The result is symbolised by:
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