74 



Fig. 4. Pressure- time curve of a 

 TNT explosion at 500 feet depth. 



Fig. 5. Low- frequency part of the 

 Fourier energy spectrum of an ex- 

 plosion at 500 feet depth. 



■at 



2/(a^ + W^), where W is 



by p = PqB °'^ and whose energy spectrunn is given by P ' 

 the angular frequency in radians per second. 



Figure 6 shows the complete energy spectrum expressed logarithmically 

 to encompass the great range of energy and frequency. The two solid parts of 

 the curve represent calculated portions. The dashed central part is the estimat- 

 ed average of the irregular oscillating part. Figure 7 gives the cumulative en- 

 ergy spectrum, i.e., the total integrated energy in all frequencies below the fre- 

 quency shown in the abscissae. 



From Figures 5, 6, and 7 it can be seen that the most prominent feature 

 of the spectrum is a peak at a frequency approximately equal to the reciprocal 

 of the interval between the initial pressure pulse and the first bubble pulse. 

 This is called the bubble-pulse frequency. Approximately one-fifth of the total 

 radiated sound energy is contained in this peak. Although pressure-time curves 

 for depths other than 500 feet are unavailable, and hence the energy spectra are 

 unknown, it appears reasonable to assume that the low frequency peak will oc- 

 cur at bubble pulse frequency for all charge depths. 



Fig. 6. Complete Fourier energy 

 spectrum. 



Fig. 7. Cumulative energy spectrum. 



