MEASUREMENT OF PRESSURES 167 



time of the wave across the gauge suffices to explain the general fea- 

 tures of the response. 



In measurements of explosion pressures one is interested of course 

 in the response to a transient pressure rather than a sustained sinusoidal 

 wave. The calculation for a circular disk with its face perpendicular 

 to the wave front can be made by elementary methods for given forms 

 of the transient. For mathematical convenience the response has been 

 calculated for a suddenly applied step pressure Pm and for a saw-tooth 

 wave for which 



, t < x/c\ 



= pJl- ^^=/^l' i > ^/c) 



This linear decay can be taken, to a sufficient approximation, to repre- 

 sent the initial portion of a shock wave. The response S{t) for a step 

 pressure has the form 



= , ^ < -a/c 



S(t) fip sin (p cos (p' 



KAPr 



[ip sin <^ c 

 TT TT 



) —a/c < t < a/c 



= 1 ) i > «/c 



where (^ = co8~^{ — ct/a) 

 The response T(.t) to the saw-tooth wave can be written 



= , t < — a/c 



T(t) _ r<P _ sin (p cos (p _ a /sin (p ip cos ip sin^A' 



KAP^ " \j: TT C0 V TT TT ~ StT /_ 



— ajc < t < a/c 

 = 1 - t/e, t> a/c 



where the origin of time is taken to be the value for which the front of 

 the wave is at a: = 0. The relative response T{t)/KAPm is plotted in 

 Fig. 5.9 as a function of the reduced time t/d for various values of the 

 ratio a/cd. The general feature of these curves is what one would 

 intuitively expect : a rounding of the initial discontinuity followed by a 

 closer approach to the true curve {a/cO = 0) as its rate of change de- 

 creases. The most serious differences occur for pressures at or near 

 such shock fronts, which therefore determine the upper limits on gauge 

 size for a tolerable error. For example, if one wishes to measure the 

 peak pressure of a shock wave with a decay constant 6 = 400 micro- 



