54 Lecture 3 
TABLE 3.1]. Pulse-Shape Relations 
Spectrum level 
proportional to 
Example Schematic shape of Lowest derivative 
number typical pressure pulse that is Zero at 
Frequency 
band 
3.4, DESCRIPTION OF UNDERWATER EXPLOSIONS 
The characteristics of underwater explosions are well established. Cole [3] 
and Underwater Explosion Research [8] may be given as general references and 
Weston [10] as a reference for acoustic effects. Upon detonation, the explosive 
is converted to incandescent gas at a very high pressure, and a shock wave is 
radiated into the water. The gas bubble expands and due to water inertia over- 
shoots its equilibrium radius; at its maximum radius the radiated pressure is 
slightly negative. The bubble now contracts, and in fact undergoes a damped 
radial oscillation. At each bubble minimum a further positive-pressure pulse 
is radiated, though only the first two of these bubble pulses are of much signifi- 
cance. 
When the shock wave reaches the surface it is reflected as a tension wave, 
which may cause cavitation. For moderate shocks the surface shows corruga- 
tions, sometimes known as the black ring, and for stronger shocks a spray dome 
is formed. The precise mechanisms are still uncertain, but the critical depth for 
corrugations over a 1-lb TNT chargeis (ub fathoms, suggesting a water-breaking 
