250 
Sec. 19 ~59- Eq.10¢ 
Fig. 19-1. The reflected wave is also a compressional shock wave but it 
moves against the mass motion of the fluid and leaves the fluid behind it 
at rest. Its velocity is given by the expressions 
Dref. = -{-w x Ve AP5 - Pp )/(Ve - v5) | : 
O=-wt /(Pz - Po) (Vo - Vz ) , Es - Eg =(1/2)(Po + Pz ) (Vo - Vg 8 G09: 
PAE TAT. Me og 
Pp. Vv Ix Dd, V fi ~ 
Lys 1» \ 3» 3» ~ 
x|U, = 0 NUS Ot uPa Ss 
/ N / V4, =o , 
| [Pex ¥as Sf Danes wets ms Fig. 19-1 
jess S 
t 
Further reflections will take place from the piston, if it is rigid, 
as ghown. The waves going in the negative direction will have lower speed 
(relative to fixed axes) than the forward waves, because they go in the 
direction opposite to the piston motion. As the fluia becomes more and more 
compressed (note that it does so in discontinuous steps in this case), the 
velocity of the waves increases. 
If the rigid wall is replaced by a second medium of infinite extent, 
a shock wave will be transmitted into this second medium and either a shock 
or a rarefaction wave will be reflected. Across the boundary there must be 
equality of pressures and of mass velocities. 
Let urbe the mass velocity and Po the pressure in the first medium 
before reflection and let P4 be the pressure which would be produced in 
medium II by a piston with velocity 4% Then: 
If Ps Po shock wave reflected 
or) 
18 re <P, rarefaction weve retlected. 
This result has been proven wigorously for ideal gases by von Newnann?® 
but seems reasonable for any media. 
WAL Bal Se Pg, V3', UZ 
NPs, V5, Ug 
\ Fig. 19-2 
/ Pe, V2; 
fg =e 
