1311 
It is useful in discussing interaction on the basis 
of these theorems to construct for any given state a W transi- 
tion-curve for waves toward the right (cf. fig. 5a) and a W 
transition=-curve for those to the left (cf. fig. 5b). 
Fig. 5 
t f 
Aka 
AY.) 
VW V 
For example, let us now consider the head-on 
collision of two shocks Sjand So. It is required to determine 
the final state of the intermediary region, given its initial 
state (po, ,, Vo) and the strengths iF and in (for definiteness 
5 is taken less than 5 ). Evidently (cf. the illustrative 
example for water in fig. 6a) a common Ve and Po exists 
only for the intersection of the upper branches of the W 
transition-curves through the initial V,p points. In other 
words, the origiial colliding shocks result in two new shocks 
receding from each other. Thus symbolically we may write 
S; Se-Sz Sq 
= -_ _— —> 
It is to be noted that because of the assumption of 
no entropy change the condition of pressure equality between 
two regions implies density equality also, i.e., no contact- 
8) 
discontinuity can exist in this case. In a similar fashion 
- 23 = 
