SHOCK WAVE MEASUREMENTS 261 



the stem, or shock front of greater strength than either of the fronts 

 OY^ O'Y. A similar situation is possible at the other end of the charge 

 also, as sketched. This possible mechanism of forming multiple shock 

 fronts is unproved for shock waves underwater, but has been quite 

 definitely established in air blast tests. It further seems quite reason- 

 able that intersections of shock waves of different strengths must occur 

 in irregular shapes of charges. If this happens, the necessary con- 

 tinuity of pressure in the absence of a shock front requires that an extra 

 shock front, or fronts, develop to establish this continuity. 



7.8. Reflection of Shock Waves at Boundary Surfaces 



The pressure-time curves and similarity curves for shock waves dis- 

 cussed in preceding sections represent the pressure distribution around 

 explosive charges in free water, that is, in regions sufficiently far from 

 boundaries that the pressure is unaffected by their presence. In all 

 actual cases, the medium is only of finite extent, being limited in any 

 case by the surface of the water and bottom, if not by walls or other 

 obstructions. It is therefore necessary to consider the possible effect 

 of the natural boundaries for any conditions, and other limits, such as 

 targets or walls, may be equally or more important. Of the various 

 boundaries of interest, the free surface of the water in contact with the 

 atmosphere is the simplest and will be considered first. 



A. Surface reflections. The reflection of a pressure wave at a free 

 surface results from the requirement that the pressure above the surface 

 be unchanged, and the reflected wave must therefore be one of negative 

 pressure, or rarefaction. In the acoustic approximation, the wave is 

 reflected as light would be from a mirror. It is convenient in consider- 

 ing the pressure at points below the surface to think of the reflected 

 wave as arising from a fictitious second source of equal strength located 

 on the other side of the surface from the actual source at the position of 

 its optical image. The pressure at any point below the surface is then 

 for waves of small amplitude simply the algebraic sum of the pressures 

 in the two waves, taking into account the difference in amplitude and 

 time of arrival. 



The resultant pressure obtained by addition is the same as the origi- 

 nal wave until the arrival of the negative reflected pressure at a later 

 time. Although this negative peak is smaller than the positive peak, 

 it is superimposed on a later weaker part of the positive wave, and the 

 resulting pressure is usually less than the initial hydrostatic value, as 

 shown in Fig. 7.21. The exact values of absolute pressure so obtained 

 depend of course on the rate of decay of the direct wave, path dif- 

 ferences, and the depth, but in nearly all cases a negative absolute pres- 

 sure is predicted for explosive waves of short duration (the absolute 

 pressure is ©f course gauge pressure plus hydrostatic pressure Po). 



