200 MEASUREMENT OF PRESSURES 



The frequency response requirements are frequently rather severe, 

 both at low and high frequencies, and can best be made evident by 

 simple examples. Faithful reproduction of the initial discontinuous rise 

 and rapid decay of shock wave pressures makes necessary sufficiently 

 rapid response that the peak value will not be rounded off appreciably. 

 In many cases the initial behavior of shock wave pressure P{t) 

 is satisfactorily represented by a negative exponential of the form 

 P{t) = Pme~^/^, where Pm is the peak pressure and the time constant 6 



10 



^ 0.6 



O 

 0. 

 V) 



lij 0-4 



> 



0.2 



00 



OjO 0-2 04 0.6 08 1.0 1.2 1.4 



REDUCED TIME t/9 



Fig. 5.24 Effect of amplifier high-frequency cutoff on an exponential pulse. 





has values from a few microseconds to a millisecond. In a simplified 

 analysis of amplifier characteristics, the loss in high frequency response 

 arises from shunting of a load resistance i?, across which the voltage 

 response is developed, by circuit capacitance C The relative response 

 F[jbi) of such a circuit at frequency / = co/27r is given by 



where the time constant r = RC. 



The transient response R{i) to the exponential P{i) is readily shown 

 to be 



m) = 



1 - r/d 



[e-^/o - e-'/r] 



