266 SHOCK WAVE MEASUREMENTS 



Osborne (80) has found that the presence of air bubbles in coatings 

 or on the faces of pressure gauges causes distortion of the initial portions 

 of weak shock waves from very small charges. It is possible that the 

 collapse of such bubbles or some other instrumental difficulty is re- 

 sponsible for the apparent rise time at these low pressures levels with 

 large charges. This explanation, however, is not easily reconciled with 

 the rapid initial response indicated at the first arrival of both the direct 

 wave and its surface reflection, nor Avith the fact that calibrations of 

 gauge sensitivity at even lower pressures by acoustic waves (see section 

 5.7) are in agreement with calibrations at pressures of several thousand 

 pounds per square inch. 



Osborne has measured pressures from Number 6 detonators at dis- 

 tances from 1 foot to 32 feet, using very small gauges found not to ex- 

 hibit the peculiarity mentioned (see section 5.6 for a description). The 

 measured peak pressures from 1,200 Ib./in.^ down to 45 lb. /in.- were 

 compared with the asymptotic pressure-distance relation of the Kirk- 

 wood-Bethe theory. Their result that the peak pressure should vary 

 as (l/R) (log R/a^~'^''^, where ao is the initial charge radius, rather than 

 as \/R, and the data were found to confirm this prediction within ex- 

 perimental error. This result is spoiled by the fact that no measurable 

 increase in duration with distance was observed, although the same 

 theory predicts an increase as (log R/aoY'^, which requires an increase 

 in duration of at least 25 per cent from 1 foot to 32 feet. Quite apart 

 from the fact that measurements on larger charges unmistakably show 

 increased durations, departures from the acoustic peak pressure vari- 

 ation without corresponding changes in duration are difficult to under- 

 stand theoretically. It is important to realize, however, that accurate 

 measurements of pressures lasting from 10 to 30 microseconds from so 

 small a charge as a detonator cap, containing less than a gram of ex- 

 plosive, are extremely difficult, particularly near the charge. 



The possible instrumental difficulties and scarcity of data make 

 generalizations as to the true form of shock wave pressures below 

 100 lb./in.2 impossible at present. The predictions of the Kirkwood- 

 Bethe theory indicate small but significant effects of finite amplitude at 

 even lower pressures but their validity can be regarded only as probable 

 and not proved. At these low pressures, however, long distances of 

 propagation are involved for appreciable percentage changes in pres- 

 sure, and for such long paths the mechanism of dissipation by viscosity 

 of the fluid must be considered. The effect of viscosity on weak sinu- 

 soidal sound waves to which acoustic theory may be applied is well 

 known to cause an absorption which increases rapidly with frequency 

 of the wave and for plane waves leads to an attenuation which increases 

 exponentially with the range. 



A transient wave, as is generated by an underwater explosion, can 



