249 
Sec. 19 -30- 
Here the sharp detonation front is immediately followed by the rarefaction 
wave. The gas in front of the detonation front is at rest, immediately be- 
hind it has the velocity w, and this velocity falls off until the end of 
the rarefaction wave is reached, after which the gas is at rest. 
It should be pointed out that this limiting case provides no mechanism 
for starting the detonation. It does illustrate, however, a situation close 
to that of an explosive detonated by a short sharp blow on an end otherwise 
blocked off by an immovable partition, 
Another difference from the usual shock wave case is the fact that the 
products of an explosion are ordinarily mixtures in which various chemical 
equilibria can occur. As the gas cools off on decompression, these 
equilibria will shift, at least until the temperature falls so low that the 
equilibria become "frozen", These shifts cause changes in C,, the heat 
capacity. 
If the detonation front is not infinitely steep, and it of course can 
not be in reality, there is the possibility that the rarefaction wave may so 
cool the sases that the reaction is stopped before complete detonation has 
taken place, thus weakening the explosion. This may be the reason why the 
mode of detonation is important. Poor detonation may cause the rarefaction 
wave to follow too closely behind the detonation front. If the rarefaction 
does cut off the end of the detonation, it should reduce the detonation 
velocity, because it vrevents complete chemical reaction. 
As the detonation proceeds down a stick of explosive, the detonation 
front should be unchanged but the width of the rarefaction wave increases. 
This may account for observed differences in effect for different lengths, 
since the region of high pressure and velocity will increase in length as 
the detonation proceeds. 
Quantitatively, the rarefaction wave back of the detonation wave can 
be treated by a procedure exactly similar to the simple rarefaction wave 
discussed in Sec, 15. Provided the equation of state of the product gases 
is known a complete solution can be obtained for any given deceleration of 
the piston, Practically, though, the qualitative results already outlined 
contain most of the useful information, inasmuch as the "deceleration of the 
piston" in the actual case is unknown and is determined by the mode of 
initiation of the detonation. 
19. Phenomena at Boundaries: Reflection 
Reflection plays a very important role in the initiation of shock waves 
by an accelerating piston, in the dying out of a shock wave due to its over- 
running by a rarefaction wave, in the effect of shock waves on an obstacle, 
and on the initiation of a shock wave by an explosion, In this section 
will be given the beginnings of the treatment of reflections. 
The simplest case is that of a compressional shock wave reflected from 
a rigid wall. The solution which satisfies all the requirements is shown in 
