174 



EXPLOSIONS AS SOURCES OF SOUND 



amount of a propellant ; for this reason nearly all the 

 material to be presented in these chapters concerns 

 sound generated by high explosives. 



Let us therefore consider what happens when a 

 quantity of high explosive is set off under water. 

 First, detonation is initiated at some point of the 

 explosive; this may be done, for example, by using 



BOUNDARY OF GAS BUBBLE 



EARLY STAGE 



SHOCK FRONT 



DISTANCE FROM CENTER OF EXPLOSION 



r 



■BOUNDARY OF GAS BUBBLE 



WATER 



LATER STAG^ 



RESIDUAL FLOW 

 I AROUND BUBBLE 



\ ' ■ 



SHOCK WAVE 



SHOCK FRONT 



DISTANCE FROM CENTER OF EXPLOSION 



Figure 1. Pressure distribution in the water at two 

 instants of time following detonation of a charge of 

 high explosive. 



a detonating cap containing a small quantity (about 

 a gram) of an especially sensitive explosive traversed 

 by a fine wire which can be suddenly heated to 

 incandescence by a current of electricity. From the 

 point of initiation a detonation wave spreads out in 

 all directions through the explosive with a velocity 

 of several thousand meters a second. In front of the 

 detonation wave the material is in exactly the same 

 state as before the explosion, while behind the wave 

 front it is gas at a pressure of ten to a hundred thou- 

 sand atmospheres and a temperature of several thou- 

 sand degrees centigrade. When the detonation front 

 reaches the boundary between the explosive and the 

 water, this pressure is transmitted to the water, and 

 a wave of intense compression starts outward through 

 the water. If the pressure were not so enormous, this 

 wave would be an ordinary sound wave. However, 

 because of its great amplitude, the wave differs in a 

 number of ways from ordinary sound waves and is 

 called instead a shock wave; it bears somewhat the 

 same relation to sound waves that a large breaker on 

 the beach bears to an ordinary water wave. A shock 

 wave is characterized by an almost discontinuous rise 

 of pressure to a high value at the front of the ad- 



vancing wave and travels with a speed greater than 

 the normal velocity of sound. The reasons for these 

 characteristics will be discussed in the following 

 sections. 



The pressure in the shock wave from an explosion 

 dies off fairly rapidly behind the shock front, and 

 by the tinie the shock wave has advanced to a dis- 

 tance of the order of ten times the radius of the origi- 

 nal mass of explosive it has become a fairly well 

 localized disturbance, advancing outward and prac- 

 tically independent of the motion of the water and 

 gas in regions nearer to the center. Figure 1 shows 

 schematically how the pressure may be expected to 

 vary with distance from the original site of the ex- 

 plosion at two successive instants of time as this 

 state of affairs is becoming estabUshed. 



Although in these later stages it no longer affects 

 the main part of the shock wave, the motion of the 

 gas-filled cavity and the water immediately around 

 it is by no means unimportant. At times such as thoss 

 shown in Figure 1 the pressure in the gas cavity, 

 hereafter called the bubble, is still quite high, and the 

 water around it is rushing outward with a very high 

 velocity. Because of the inertia of the water, this out- 

 ward motion continues long after the force of gas 

 pressure, which initiated it, has become negligible. 

 As the gas bubble expands, the pressure in it drops, 

 and eventually becomes far less than the normal 

 hydrostatic pressure of the surrounding water. This 

 excess of pressure on the outside finally brings the 

 expansion to a halt, but not until the bubble has 

 reached a radius which may be several dozen times 

 the initial radius of the explosive. A contraction now 

 sets in, and again, because of the inertia of the water, 

 the bubble overshoots its equilibrium radius and the 

 contraction does not stop until a very high pressure 

 has been built up in the gas bubble. Several cycles of 

 this expansion and contraction may take place before 

 the oscillation dies out. The period of these bubble 

 oscillations is of the order of a thousand times the 

 duration of the pressure which the shock wave exerts 

 as it passes a particular point in the water; it is usu- 

 ally of the order of 1/30 to 1 sec, depending on the 

 size of the charge and its depth. At each contraction 

 a new pressure wave is sent out into the water; these 

 so-called "secondary pulses" are many times less in- 

 tense than the shock wave, but as they have a 

 duration many times longer, they may contain a 

 greater amount of impulse, and a comparable though 

 smaller amount of energy. A quantitative theory oi 

 this phenomenon will be sketched in Section 8.6. 



