190 



EXPLOSIONS AS SOURCES OF SOUND 



be about half of the quantity (30). In between the 

 end of the tail of the shock wave and the beginning of 

 the tail of the first bubble pulse there is a long period 

 during which the pressure is below normal; this period 

 occupies most of the time consumed by the first 

 oscillation, and the negative impulse delivered during 

 it is just equal to the expression (30). For most ap- 

 plications, however, this negative pressure and the 

 tail parts of the shock and bubble pulses can be 

 neglected. 



In cases where migration of the bubble is slight, 

 the bubble pulses show a fairly regular rise and fall of 

 pressure. When migration is rapid, irregularities are 

 more apt to occur, and sometimes two or more fairly 



DISTANCE ESM ■ E H = Tj 

 DISTANCE EH = r 



Figure 9. Superposition of direct and surface- 

 reflected pulses. 



well-separated peaks are observed.^* It has been sug- 

 gested that these multiple impulses may be due to 

 breaking of the bubble into several separate bubbles, 

 which emit distinct pressure peaks in the contracted 

 stage, but which coalesce when they expand again. 

 A few typical oscillograms of bubble pulses, taken 

 from references 23, 24, and 29, are shown in Figure 8. 

 The first bubble pulse is usually by far the strongest ; 

 for small charges as many as eight or ten pulses have 

 been counted, but for large charges usually only two 

 or three bubble pulses are measurable. For some 

 reason, a charge fired on or very close to the bottom 

 usually gives a very weak bubble pulse, and the 

 number of measurable pulses is less than for shots 

 in open water. 



A caution should be added concerning the inter- 

 pretation of oscillograms of bubble pulses; because of 

 the relatively long duration of these pulses the nega- 

 tive pulse reflected from the free surface of the water 

 will often overlap the direct pulse, making the re- 

 corded pressure appreciably different from that due 

 to the direct pulse alone. The statements given 

 previously apply to the latter only. 



8.7 SURFACE REFLECTION AND 



CAVITATION 



When a hydrophone is placed in the water at some 

 distance from an explosive charge, the shock wave 

 and secondary pulses received are modified by reflec- 

 tion at the free surface of the water. This reflection 

 is most conveniently described by the principle of 

 images, which we have encountered in another ap- 

 plication in Section 2.6.3. This principle is applicable 

 whenever the pressure amplitudes are small enough 

 for the laws of ordinary acoustics to apply. Referring 

 to Figure 9, the pressure produced at any instant at 



PRESSURE -TIME CURVE WHICH WOULD BE 



OBSERVED IF WATER DID NOT CAVITATE 



■PRESSURE- TIME CURVE AS MODIFIED BY 



CAVITATION 



Figure 10. Modification of a surface-reflected pulse 

 by cavitation. 



a hydrophone H by an explosion or other source of 

 sound at E is the sum of the pressure due at that 

 instant to the direct wave EH and the pressure due 

 at the same instant to the reflected wave E&H. Ac- 

 cording to the image principle, the latter pressure is 

 exactly equal to the negative of the pressure which 

 would be produced in the absence of a surface by a 

 source E' which is the mirror image of E in the sur- 

 face and which has the same time variation. If z^ is 

 the depth of the explosion, z^ the depth of the 

 hydrophone, and x the horizontal range, the path 

 difference between these two waves is 



Ti — n 



V(2, + Sa)2 + X" - Viz, - Z^y + X' 



43e2A 



(31) 



n + Ti 



When the distance ES from the explosion to the 

 portion of the surface at which the reflection takes 

 place is so small that the incident pressure at S is ap- 

 preciably in excess of one atmosphere, the simple 



