MEASUREMENT OF PRESSURES 



193 



and a standard condenser of known capacitance. The standard con- 

 denser is conveniently made the terminating condenser in the termi- 

 nating networks described in part (A) of this section. A step voltage 

 applied to this condenser in series with the cable then gives a response 

 curve similar to the sketch in Fig. 5.21(a), the gradual falling off with 

 time being the result both of dielectric effects (change in capacitance 

 with frequency and dielectric loss) and of leakage resistance of the cable 

 circuit. The transient characteristic thus obtained is actually a com- 

 plete calibration of the charge sensitivity of the complete electrical cir- 

 cuit (including the recording circuit), except for times so short that 

 transient effects in long cables are of importance. That this is true 

 can be seen from the equations derived in section 5.7, as the capaci- 



(a) STEP VOLTAGE 



(b) EXPONENTIAL 



Fig. 5.21 Effect of dielectric loss and leakage resistance of cables on transient 



response. 



tance C representing the circuit capacitance can actually be a fictitious 

 equivalent capacitance (real or complex) of any two-terminal network. 



For rapidly changing signals, such as the initial peak pressure in a 

 shock wave, the initial response is evidently the correct one to use, and 

 for more slowly changing signals correspondingly later values of re- 

 sponse. The exact formulation of the relations can be made by the 

 superposition theorem, which relates the response of a linear system for 

 any apphed function to its value for a unit function or "step voltage." 

 The nature of the error for an exponential pulse is indicated in Fig. 

 5.21(b), drawn roughly to correspond with the step response indicated 

 in Fig. 5.21(a). It is seen that the deviations from the ideal response 

 become increasingly great with time, hence errors in area measurement 

 (to give the impulse of a pressure-time curve) can be serious for rela- 

 tively small loss in step response. If, however, this loss in step re- 

 sponse is small, quite adequate correction for it can be simply made. 



Consider the case of an applied voltage V{t) = Yoer^'^ and a step 

 response of the form S{f) = >Sc» + {So — S-x,)e~^/^, corresponding to an 

 initial response So followed by an exponential decay of time constant r 



