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Notes: It has been clarified in an earlier work [Y. Sano, J. Appl. Phys. 65, 3857 (1989)] that the locations of attenuating peaks in smooth strain, particle velocity, and stress profiles in a smooth plane-wave front differ, that is, the order of peak precedence is stress, particle velocity, and strain. As a result of the precedence order, the wave front composed of elementary waves such as a contraction wave C, mesocontraction waves I and II, and a vice-rarefaction wave R was formed. That the process is degraded by another rarefaction wave Rb which first follows the wave R, and then outruns the waves R, II, and I in sequence, has also been proved. [Y. Sano, J. Appl. Phys. 67, 4072 (1990)]. After the completion of the degradation process, the wave front, i.e., the wave C, may attenuate little, but steepen. This paper extends the process under consideration to include the steepening process during which the wave C approaches a steady state. In addition to this extension, stationary phenomena in strain, particle velocity, and stress-time profiles are shown to be able to take place in the degradation process. It is one of the main purposes of this paper to show through the phenomena that the response caused by the wave fronts during the process will be unsteady and nonequilibrium. Furthermore, universal properties of the stress-particle velocity paths are clarified. The properties involve concavity or convexity of the path curves produced by the waves C, I, II, and R. Universal properties of the stress-strain paths such as concavity, convexity, or inflection of the path curves by the waves C, I, II, and R are also clarified. Through the behavior of the stress-particle velocity and stress-strain paths having the properties mentioned above, it is also shown that the response caused by the waves will be unsteady and nonequilibrium. The stationary phenomena, the universal properties, and the stress-particle velocity and stress-strain behaviors are compared with the previous experiments and computational data. Another main purpose of this paper is to confirm through comparison the occurrence of the elementary waves and the degradation process in the experiments.