MEASUREMENT OF PRESSURES 



165 



gauge on its measurement of pressure and disturbance of the pressure 

 to be measured must therefore be considered. 



The simplest analysis bearing comparison with reality is that of the 

 effect of finite gauge area.^ Neglecting for this analysis any internal 

 reflections or diffraction of the pressure wave by the gauge, we may 

 consider the steady state response of a thin circular disk to a sinusoidal 

 pressure acting on its face. If we let the response of unit area to a 



ixJ 



z 



£ 



in 



UJ 



q: 



UJ 



> 



UJ 



1.5 



1.0 



05 



0.0 



-05 



0.01 0.03 0.1 0.3 1.0 3.0 



REDUCED FREQUENCY (f/OC) 



Fig. 5.7 Effect of finite gauge size on frequency response. 



pressure P be KP and assume a pressure Pm cos 2'kx/\ where X is the 

 wavelength, the response R{\) of a disk of radius a is found by direct 

 integration to be 



R{\) = K{ira')Pr 



2Ji(27ra/X) 

 (27ra/X) 



where Ji{X) is Bessel's function of the first order. This result is for a 

 standing w^ave. Letting X = c/f, where c is the velocity of the wave 

 and / its frequency, we obtain for the response to a wave P{t) = Pm cos 

 2Tft, travelling parallel to the face of the disk, 



(27r/a/c) 



(5.12) 



^ The analysis which follows is based on a report by Arons and Cole (3) , 



