CHRISTIAN: THE ACOUSTIC OUTPUT OF EXPLOSIVE CHARGES 



treatment of explosion data, where we usually study only narrow-band 

 slices of the spectrum taken near selected frequencies, we may forget 

 the oscillatory character of the spectral energy distribution. We 

 find the highest spectral energy at the so-called "bubble fundamental 

 frequency," which corresponds to the first bubble period spacing in 

 the time function. We find minor irregularities in the spacings of 

 the first several harmonics while the second and third bubble pulses 

 are getting shaken out. And after a while, the pattern stabilizes, 

 and we have a regularly spaced series of peaks and nulls. I must 

 point out that true nulls are in the spectrum, even though they are 

 not conspicuous at the higher frequencies in Figure 2. This is a 

 computer-generated plot. The computational grid size used and the 

 characteristics of the plotter control details of the picture. Lest 

 you hope to find these oscillations smoothing out at long ranges, 

 or start thinking of clever ways to clean up the source level curve 

 by smoothing or filtering (e.g., Skretting and Leroy, 1971), let me 

 show you one of Gordon Hamilton's sonagrams of signals recorded some 

 500 miles from explosions (Figure 3) . The horizontal axis is time 

 and the vertical axis is frequency (0 to 500 Hz) , Those alternating 

 light and dark horizontal bands corresponding to no-energy and high- 

 energy show that neither distance nor manipulation can smooth out the 

 true source spectrum. 



Naturally we are going to have problems in fitting explosion 

 source levels into the sonar equation, where quantities are added 

 and subtracted in a comfortable linear fashion. The translation of 

 "compatibility with the sonar equation" into more explicit prosaic 

 terms is sijmmarized in Figure 4. What we mean is that we wish there 

 were no finite amplitude effects; no nonlinearities; no inherent 

 change in wave shape or frequency distribution as the wave propagates 

 outward, so that all observed changes could be ascribed to the medium. 



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