181 
21 IV. EFFECTS OF PRESSURE WAVES 
2. SMALL TARGETS 
From Equation [21b] in Appendix II we find that a gas globe from 1600 pounds of ama- 
tol under 60 feet of water might perhaps expand to a maximum radius of 30 feet. Then 
we have 47x 30°/3 cubic feet of water displaced outward over a sphere of radius 126 
feet, requiring a linear displacement of the water of magnitude 
An - 3 
—— = 0.57 foot = 7 inches 
4m - 126? 
This displacement is of the same order of magnitude as the indentation in the mine 
case. Nevertheless, the afterflow cannot have had anything to do with the crushing 
action, for it occurs in too leisurely fashion, requiring over a quarter of a second. 
The pressures due to the afterflow must have been quite negligible. 
IV. EFFECTS OF PRESSURE WAVES 
3. LARGE TARGETS 
3. TARGET LARGE RELATIVE TO THE SCALE OF THE WAVE 
At the opposite extreme, when the target is large as compared to the thick- 
ness of the wave, the water has no time to escape sideways, and adjustment to the 
presence of the target must be made on the spot. Relatively large modifications of 
the water pressure may then occur. The appropriate ideas to use in considering the 
impact of the wave upon a large target are those associated with the reflection of 
waves. 
In order to throw some light upon the complicated phenomena to be expected, 
a number of simplified cases will be discussed which are amenable to analytical 
treatment. 
IV. EFFECTS OF PRESSURE WAVES 
4. IMMOVABLE INTERFACE 
4. REFLECTION AT AN IMMOVABLE INTERFACE 
Consider a plane wave in water falling at an angle of incidence 6 upon the 
plane face of a target consisting of homogeneous material of a different sort, gas- 
eous, liquid, or solid. Let the wave be of sufficiently low intensity so that acous- 
tic theory can be used. 
Then at the interface between water and target the incident wave will di- 
vide into two, a transmitted wave which continues into the target at an angle of re- 
fraction 9, and a reflected wave which returns into the water. Let the pressure and 
particle velocity in the incident wave be p,u, in the transmitted wave p',u’, in 
the reflected wave p”, u”. Let the density and the speed of sound in water be p, and 
¢,, respectively, and in the material of the target, p, and c, (Figure 9). 
Then according to the usual laws for the reflection of sound waves (Appendix 
I, Section 2, Equations [9a], [9b] and [10]), 
c,sin@ = c,sind’ [1] 
