246 
Sec. 17 De 
D Ya Figs: LiL 
red 
Then it will be shown that the rarefaction wave which is started by the de- 
celeration of the piston will overtake the shock wave and weaken it. The 
shock wave will therefore travel with constant velocity until overtaken by 
the front of the rarefaction wave, whereupon its velocity and intensity 
will be continuously reduced, presumably until an ordinary sound wave results, 
Therefore, even a plane shock wave in a medium with no viscosity or thermal 
conduction will die out unless it is continuously supported by a moving 
piston. This result may not be new, but we have not noticed it so far in 
the literature. The spherical case has not been treated but presumably 
would show a falling off greater than the inverse square. 
Two arguments support this conclusion for plane shock waves. The 
first is a thermodynamic one. The comvression of the medium which occurs 
when the shock front passes a given material point is an irreversible 
process---the material is shifted from one adiabatic to another in the 
process, Consequently energy is continually being degraded. But if the 
piston is ultimately brought to rest, only a finite amount of work is done 
by the piston on the column of materiai so that this work must ultimately 
be degraded to heat by the irreversible process. The shock wave cannot 
therefore continue indefinitely unaltered. 
The Second argument is more detailed, The rarefaction wave should 
behave exactly as the simple rarefaction discussed in Sec. 15 except that 
the velocity w is superimposed. Its front should thus propagate with a 
velocity w +c, where c is the velocity of sound in the compressed, heated 
gas back of the shock front. Tho shock wave itself travels with a slower 
Speed than this, This is shown for the perfect gas case by inspection of 
Table 4-1, in which (D/a) - (w/a)<1 or D-w<a. But cya decause 
of the higher temperature. For a more general proof reference may be made 
to Sec. 5, There it was shown that if the final state of the medium is 
above the point of tangency J on the Hugoniot curve, the velocity of detona- 
tion is less thanw+ c. But in the shock wave case the initial point A 
(Fig. 5-1) lies on the Hugoniot curve, rather than below it as in the detona- 
tion problem. Consequently the only point of tangency is A itself so 
that the final state for any shock wave must be above tlie point of tangency 
and therefore the velocity is less than w+ c and consequently less than 
that of the rarefaction wave. Duhem has also discussed this. 
