836 
36 ING 13% 
4 i 
Ft Dd 
Bae 
STEP RESPONSE, Rit) 
1.0 ° +1.0 
REOUCED TIME, (ct/a) 
Fic. 5. Response of a gauge of radius a to a progressive step wave 
of velocity c. 
time required for the gauge to give maximum response, 
this time being theoretically equal to 2a/c. 
The validity of such a correction involves the as- 
sumptions that distortion due to diffraction effects dies 
out sufficiently rapidly not to affect the curve after the 
maximum, and that the true pressure curve is suffi- 
ciently simple for a linear decay law to be a good ap- 
proximation. It is reasonable, however, to expect that 
any diffraction effects will have the general character of 
damped transient oscillations about the gradual rise as 
the gauge is covered by the advancing wave and should 
not be significant after the gauge is covered. Whether or 
not the pressure curve is sufficiently simple to be repre- 
sented by a straight line or smooth curve, depends, of 
course, on experimental conditions. Unless appreciable 
interference or reflections are combined in the resultant 
wave, the corrected maximum pressure may well be used 
as a significant measure of the wave. 
This principle has been extensively applied by the 
UERL group in the interpretation of underwater shock 
wave records and the estimation of true peak pressures 
under conditions where the gauge size introduced ap- 
preciable error. It was found that the simplified theory 
ARONS AND R. 
He COLE 
provides adequate correction for amplitude effects up to 
about 10 to 15 percent, but then begins to show serious 
departures from observed values. It has also been found 
empirically that the gauge radius a which must be used 
in the theory is not the radius of the element alone, but 
rather the radius of the complete gauge including coating 
material. 
B. Interference Effect 
The analysis of the effect of gauge size on transient 
response neglected any disturbance of the pressure wave 
due to presence of the gauge in the field. Actually, of 
course, the gauge material is a medium through which 
sound waves can be transmitted. As a result, one can 
expect interference effects due to repeated internal re- 
flections of the incident wave at the interfaces of the 
crystal. This would have roughly the character of a 
damped saw-tooth oscillation. The frequency of this 
oscillation cannot be calculated accurately, but it is 
probably of the order of 100 kc/sec. for the types of 
gauges described in this paper. 
In order to examine the effect of interference on re- 
sponse of an actual gauge, we might consider a circular 
disk in either of two orientations: face-on and edge-on to 
the approaching pressure front. The Coulomb sensitivity 
of a disk of tourmaline depends only on the face area, 
not on the thickness, and, as a result, the travel time is 
obviously minimized and the natural frequency highest 
if a thin disk is oriented face-on. It is to be expected, 
however, that Bernoulli effects‘ will be much less if the 
same disk is edge-on. 
To the extent that a single very thin disk is practical, 
the face-on orientation may appear preferable because of 
the inherently higher frequency characteristic. In actual 
practice there is a limit to the thinness possible, and in 
the interest of greater sensitivity, it is desirable to con- 
struct a gauge from a pile of disks; thus multiplying the 
effective area and sensitivity and obtaining a better 
electrical and mechanical design. Under such circum- 
stances the face-on orientation would have much larger 
interference oscillations than the edge-on orientation 
and comparable transit time and flow effects. 
Fic. 6. Response of a gauge of 
radius a to a progressive saw-tooth 
wave of decay constant @ and 
velocity c. Solid line represents 
incident wave. Dotted curves show 
response for various values of a/c8. 
AMEDUCED Tear, m/e) 
