SHOCK WAVE MEASUREMENTS 263 



tion of an explosion (see section 10.3), the time interval A^ in Fig. 7.21 

 being closely equal to the value computed from the image construction 

 if the surface of the water is smooth. ^^ 



B. Bottom reflections. If the bottom of the sea could be considered 

 a perfectly rigid boundary, it would act as a perfect reflector of pressure. 

 Thus the reflected wave developed at the boundar}^ would, in the acous- 

 tic approximation, be a compression wave progressing as if it originated 

 from an image source at the position of an optical image in the bound- 

 ary of the actual source. Any real material is only imperfectly rigid 

 as far as reflection of pressure waves is concerned, and the doubling of 

 pressure at the boundary obtained assuming perfect rigidity is therefore 

 an overestimate. In order to show how effectively actual bottom ma- 

 terials reflect the energy striking them, consider the case of a charge 

 fired on the bottom. If no energy were absorbed by the bottom, this 

 charge would be equivalent to a charge of double the weight fired in 

 open water, because all the energy is confined to the water above the 

 bottom. A charge of weight 2W to sl first approximation gives a peak 

 pressure at any distance increased by a factor of 2^'^ = 1.26, and a du- 

 ration increased in the same ratio. The impulse of the wave should 

 therefore be increased by 2^/^ = 1.59^ and the energy flux density by a 

 factor of 2 for a charge fired on a rigid bottom. 



The increases in pressure and duration actually realized depend on 

 the character of the bottom, but are seldom more than 3^-% of the 

 predicted upper limits. For example, the peak pressure, impulse, and 

 energy flux density 60 feet from a 300 pound TNT charge fired on a 

 bottom of hard-packed sandy mud were increased by 10, 23, and 47 

 per cent over the values observed from a charge at mid-depth. These 

 increases correspond to increasing the weight of a charge in free water 

 by roughly 35-50 per cent rather than a factor of two, and an appreciable 

 fraction of the shock wave energy was therefore transmitted to the 

 bottom in this case. 



If the bottom could be considered to be a homogeneous fluid, acous- 

 tic theory predicts that a somewhat weaker wave of compression would 

 be reflected geometrically, the pressure being calculable from the den- 

 sities and sound velocities of the water and boundary material by the 

 formulas of section 2.8. Experimental measurements with charges fired 

 near the bottom show, however, that the situation is not this simple. 

 For example, an observed pressure-time curve 4 feet above the bottom 

 and 50 feet from a 300 pound charge fired 4 feet above a sandy-mud 

 bottom is reproduced in Plate VIII. The discontinuous shock front, 



^3 It is important to realize that the geometrical reflection discussed is strictly 

 valid only in the adiabatic approximations, and is not rigorous for waves of finite 

 amplitude. 



