CHRISTIAN: THE ACOUSTIC OUTPUT OF EXPLOSIVE CHARGES 



values." It is true, of course, that the visible problem is not as 

 great for the lowest frequencies of interest as it is for higher fre- 

 quencies. Many of the above references do not look at the very low 

 frequency end of the scale. 



SONAR EQUATION COMPATIBILITY AND PREDICTABILITY 



In order to examine the problems of sonar equation compatibility 

 and predictability, we must face up to the nonlinear nature of explosion 

 pressure waves. Before getting into that discussion, let us take a 

 brief refresher look at the time and frequency domain functions in this 

 explosion pressure field. 



Figure 1 shows two typical pressure-time histories for underwater 

 explosions, recorded with the special-purpose equipment designed for 

 such measurements. The experimental setup is shown at the top of the 

 figure. Charges were fired at depth and recorded at the s\irface above. 

 The record on the left is from a 57-pound TNT charge detonated at 

 6,600-foot depth. That on the right is from an 8-pound TNT charge at 

 2, 050- foot depth. 



These pressure-wave records show the usual high-amplitude shock 

 wave followed by the succession of pulses associated with the oscilla- 

 ting bubble of product gases. There are scaling laws for explosion 

 pressure waves of this sort, in terms of explosive charge material, 

 weight, and depth of detonation. Unfortunately (from the point of 

 view of simplicity) , these scaling laws contain different coefficients 

 and exponents for different segments of the pressure wave; and there- 

 in lies the problem that you will hear more about later. 



The frequency domain representation of an underwater explosion 

 pressure wave, such as Figure 2, is also familiar. But in our everyday 



34 



