SECONDARY PRESSURE WAVES 381 



These difficulties are particularly evident in large charge work, which 

 must usually be conducted under conditions somewhat less than per- 

 fect, and lead to errors in determining relative positions of gauge, charge, 

 and water boundaries. The total depth of water, character of the bot- 

 tom, and migration of the bubble are some of the factors not ideally 

 determined, and the consequence is scatter of the data. 



B. Problems and errors of analysis. The analysis of pressure-time 

 records is complicated by a number of factors, the most important of 

 which are choice of a reference axis for pressure and correction for the 

 reflected pressures from the surface and bottom. The experimental 

 results for pressure and derived quantities (energy flux and impulse) 

 must be measured with respect to some chosen pressure level. For com- 

 parison with theory, this value is best taken as hydrostatic pressure 

 (zero gauge pressure). An accurate determination of this level in 

 records such as the one reproduced in Plate X is simple for the shock 

 wave, but difficult for the bubble pulse because of its smooth, gradual 

 rise from values less than hydrostatic while the bubble is large. A true 

 baseline is thus not accurately defined except for times preceding the 

 shock wave, and judgment must be used in drawing a reference line. 

 The resulting errors are not large for calculation of peak pressure, but 

 may seriously affect values of impulse and energy flux density (propor- 

 tional to f{P — Po)dt and f{P — PoYdt respectively), owing to the 

 long intervals of small excess pressure which contribute large areas. 

 Errors of this kind in the investigations summarized in section 9.6 

 introduced scatter of the order of five per cent in peak pressure and ten 

 per cent in impulse and energy. 



The second problem in analysis of the recorded pressure-time curves 

 is that the pressure existing at a given point almost always is the super- 

 position of the ''direct" wave and reflected waves from the surface and 

 bottom. In acoustic theory, the pressure wave striking a free surface 

 is geometrically reflected as a wave of equal magnitude but negative 

 pressure. The resultant absolute pressure at other points is then the 

 algebraic sum of the pressure in this diverging reflected wave and the 

 pressure existing as a result of the wave travelling in a straight line 

 from the charge. It is readily calculated by simple superposition tak- 

 ing into account the later time of arrival and increased attenuation in 

 the reflected wave. The simple picture may be inaccurate if the abso- 

 lute pressure at any point becomes negative and cavitation sets in. The 

 bottom reflection occurs as a wave of positive pressure with somewhat 

 less initial amplitude than the direct wave, owing to the bottom not 

 being perfectly rigid, acoustically speaking. In addition, there may be 

 a ground wave, corresponding to signals transmitted through the sea 

 bed and re-emitted into the water (see section 7.8). The proper amount 

 of correction is thus not simply determined. 



The observed pressures in actual situations are thus those of a com- 



