1309 
HS 
Consider a finite rarefaction wave R (continuous, 
adiabatic change) moving toward the right. As before, let 
V, be the material velocity of the normalized region and V 
that of the region not normalized (1.e., on either side of the 
rarefaction), Then we have from Riemann's argument 
Put WP) = - ra es 
Then vev, + Ya) (7a 
In the case of such a rarefaction wave R traveling to the 
left 
V=vV,- Wa @) (7 
The V,p diagrams for such rarefaction waves are shown in fig. 
4c,d. | 
The functions Pn (p) and Wr (P) represent physi- 
cally the absolute change in material velocity across a shock- 
= ll te 
