171 
11 III. PRESSURE WAVE 
3. QUALITATIVE THEORY 
has sunk to p, at the l 
gas globe, should be, 
therefore, somewhat as Solid 
shown in Figure 6, in | 
which the scale of 
abscissas is reduced 
relative to that of 0 
Figure 5. 
The after- 
flow has two effects: 
The motion of the water due to the afterflow tends to modify the distribu- 
tion of pressure roughly as if by adding to it a component proportional to — yeu 
Radius r 
Figure 6 
( p= density, u = particle velocity), as in the Bernouilli equation of ordinary hy- 
drodynamics. Since u decreases in an outward direction, this effect tends to in- 
crease the pressure in the water as compared to that of the gas and so to prolong the 
pressure impulse. It can be said that an excessive amount of momentum is taken up at 
first by the water near the gas and is then paid out as this water moves outward and 
slows down. 
The second effect of the afterflow will be that a large part of the energy 
originally in the exploded material is not carried off by the pressure wave but re- 
mains behind in the water in the form of kinetic energy. Hence the water will con- 
tinue to flow outward after the gas pressure has sunk below the hydrostatic pressure; 
it will flow outward until, after the lapse of a comparatively long time, it is 
brought to rest by the action of the hydrostatic pressure. 
The gas pressure having now become very small, the hydrostatic pressure 
will start the water moving inward, and the gas globe will thus be compressed again. 
During this second stage of compression, a second intense pressure wave will be emit- 
ted. The gas globe may oscillate in this fashion a number of times. The situation 
may be compared to a mass, representing the inertia of the water, mounted on two op- 
posing springs, a powerful one, the gas, that ceases to act beyond a short distance, 
and a very weak one, the hydrostatic pressure. The weak spring will undergo large 
displacements, but, given time, it will get the mass moving inward again and so will 
eventually restore the initial state of high compression of the strong spring. 
During each of the expansion phases, negative pressures (relative to the 
hydrostatic pressure as zero) will be transmitted to a distance. Thus we are led to 
expect that observation at a distance will reveal a succession of strong pressure im- 
pulses, separated by relatively long periods, during which both positive and negative 
pressures of moderate amplitude occur. The first impulse should have a steep front, 
whereas the subsequent ones should have rounded tops and should be progressively 
weaker. 
