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APPENDIX B 
TWO PROOFS OF ONE-DIMENSIONAL INTERACTIONS 
Table 3 in the text outlines the results of one-dimensional 
interaction of shock=-waves and rarefaction waves. In this 
section we will discuss in detail several instances of wave 
interactions, in which the differences between ideal gases and 
water=-like substances are most striking. 
We shall first recall some relations existing between the 
effective pressure, material velocity, and density in front and 
behind a shock=-wave or a rarefaction wave. Consider the shock 
or rarefaction wave moving along an x-axis. The x-axis will thus 
be divided in two parts. The effective pressure, material 
velocity, and density on the right of the wave-front will be 
designated p,, V,» andp,; those on the left, Py» Vi, andP,, 
respectively. The material velocity will be considered positive 
if it is moving in a positive direction along this x-axis, and 
negative if it is moving in the negative direction. A shock or 
rarefaction wave moving in a forward or positive direction re- 
lative to the undisturbed material will be designated S and R, 
respectively; in the opposite direction, §. and R. On the basis 
of the above conventions the following inequalities hold 
Py > Pys P\>Pp for § 
Pi< Pr» P3< Py for S$ (A 
Waar Van for & or S 
Bi < Py» P1<f, for R 
P} > Pp» P1>Py for R (At 
Vai. for R or R 
