1264 
Let t be the time required for the reflection. Let I, 
and I, be the impulses of the incident and reflected 
shocks. It follows from (11.2) that 
tr, a ode (ries 
h ae -[° U, dx 
where — ‘ 
i op Pango 
2 
I, 4 fr Up aXe 
II. THE ANALYTICAL SOLUTION 
12. Consider a plane shock, S, impinging on a rigid 
Fige 7 wall, W, at normal incidence 
M, uso (fig. 7). Let the plane of the 
——_ S wall be x = O, and let the 
t M u>0 x-axis be directed toward the 
x 
ToT oncoming shock. Let the posi- 
tion of any element of the fluid 
be x = x (t%), where t is the 
x Fig. 8 time measured from the moment 
D -at which S strikes W. The 
situation is represented in the 
X, te-plane shown in fig. 8. Here 
Mo 
x D is the world line of the shock 
(x, 0) ¥e x(t) 
Xo» front after the time t = 0. The 
a t world line of a typical element, 
initially at x,, is shown with. a 
S412 
