168 



MEASUREMENT OF PRESSURES 



seconds to an accuracy of 2 per cent the ratio a/cd should not, on the 

 basis of the calculation, exceed 0.02. For water c = 1.5 X 10^ cm. /sec. 

 and the allowable radius is a = 0.02 X 1.5 X 10-^ X 4 X 10^^ = 1.2 

 cm. 



Several objections can be made to this simple analysis: first, that 

 the actual situation for a gauge of finite volume must be much more 

 complex as a result of reflection, diffraction, and Bernoulli flow around 

 the gauge; second, that orienting a thin disk with its face parallel to the 

 pressure wave front is more efficient in reducing the transit time. Any 

 very realistic attempt at a solution of the diffraction problem is of course 

 rather complicated. The effect of reflections at the gauge surfaces can 

 be seen qualitatively for a crystal gauge by considering an infinite slab 



1.0 



0.75 



0.50 



0.25 



L-t 



-0,5 



-0.25 



0.25 



REDUCED TIME t/e 



Fig. 5.9 Calculated response of a gauge of finite diameter to linearly decay- 

 ing pressure. 



0.5 



of gauge material with faces parallel to the wave front. An incident 

 step pressure wave is partially reflected at the first face because of the 

 difference in density and sound velocity of the two media, the trans- 

 mitted wave in the crystal is again partially reflected as a rarefaction at 

 the second face (assuming a gauge medium denser than water), and a 

 series of reflections of decreasing amplitude takes place. 



The integrated pressure in the slab is easily seen to resemble a 

 damped oscillation converging on the final equilibrium value, the period 

 being the time for one round trip across the slab with the velocity of 

 sound in the medium. This process is of course considerably modified 

 by diffraction for a gauge of finite extent but one might qualitatively 

 expect some roughly similar shock excitation to take place. Oscillations 

 of this kind have been observed in the response of tourmaline disks sub- 

 jected to explosion pressures, the effect being most marked if the face 



