1.11 



TESTING TECHNIQUE 



554 Quasi-Static Calibration 



For an acoustically stiff pressure-operated instru- 

 ment at frequencies low enough so that the wave 

 length is long compared to the dimensions of the 

 instrument, the response depends only on the pres- 

 sure in the neighborhood of the instrument. It is 

 independent of the type of wave giving rise to the 

 pressure, of its direction of propagation, and even 

 of whether there is a wave present at all, so long as a 

 hydrostatic pressure variation of corresponding am- 

 plitude and frequency is present. To calibrate such 

 an instrument in this low-frequency register, it is 

 necessary only to produce a known pressure variation 

 in the portion of the medium adjoining the instru- 

 ment. Several possible methods of calibration are 

 based on this principle. 



For frequencies below a few cycles per second, one 

 can bring about this pressure variation in water 

 simply by raising and lowering the device sinusoid- 

 ally through a known distance at the desired fre- 

 quency. If the depth in centimeters is h, then the rms 

 pressure in dynes per sq cm acting on the transducer 

 is 



Pgh_ 

 2\/2 



(51) 



where p is the density of water (1 gram per cu cm) and 

 g is the acceleration of gravity (980 cm per sec per 

 sec). If the test is carefully made, accurate calibra- 

 tions in this low-frequency range can be made. 



At higher frequencies, it is possible to use a tank 

 in which the pressure is varied sinusoidally through 

 known values. This can be effected by building what 

 is essentially a low-frequency transmitter into the 

 wall of a closed stiff tank. If the transmitter is of the 

 electromagnetic type, whose stiffness is low compared 

 to the stiffness of the tank in the frequency range of 

 interest, then the force exerted by the piston can be 

 calculated from the current into the projector, either 

 by measuring or by calculating the force per unit 

 current developed by the piston when it is blocked. 

 When this force is known, the pressure which it pro- 

 duces in an acoustically stiff chamber can be calcu- 

 lated. 



This method is applicable only for frequencies 

 far below those for the first chamber resonance of the 

 tank, since, as the tank approaches its lowest reson- 

 ance, its stiffness drops in value, becoming quite low 



at the first resonance. Also, at this point, pressure 

 can no longer be considered uniform throughout the 

 tank, and consequently one cannot calculate in any 

 simple manner the pressure at any desired point from 

 the force exerted by the piston. If the walls of the 

 chamber have resonances below the cavity resonance 

 of the chamber, these resonant frequencies reduce 

 even further the upper limit of the useful frequency 

 range. This method has been used with considerable 

 success by USRL with a tank of the type described, 

 built by the Bell Telephone Laboratories. 4 '-' The low- 

 est resonance frequency for this system is about 300 

 c, so that the system is useful up to about 100 c. In 

 using such a system, one must remember to avoid 

 any condition which lowers the stiffness of the 

 chamber, such as the presence of air bubbles or an 

 acoustically "soft" transducer. Over a limited range, 

 corrections may be made for decreased stiffness due 

 to any effect, provided this stiffness can be measured. 

 Other quasi-static absolute calibration methods 

 have been employed. One makes use of a condenser- 

 type hydrophone 30 in which the capacitance of the 

 condenser is in one arm of an impedance bridge em- 

 ploying a carrier frequency of 5 kc. Changes in pres- 

 sure on the diaphragm cause a variation in capaci- 

 tance which unbalances the bridge. The amount of 

 unbalance becomes a measure of the pressure. This 

 particular system is flat from to 75 c, above which 

 the effect of the first resonance of the hydrophone 

 becomes prominent. Hydrostatic pressure equaliza- 

 tion is provided to eliminate the variation of calibra- 

 tion with hydrostatic pressure. If, however, the 

 equalization cannot be carried out, then, by lowering 

 the hydrophone a known distance in water, the abso- 

 lute calibration can be obtained from the bridge 

 imbalance thus produced. Since the hydrophone is 

 known to have a Hat response up to 75 c, this direct 

 hydrostatic pressure calibration is applicable over 

 this range. 



5.5.5 



Absolute Methods Not Involving 

 Transducers 



There are several methods of establishing abso- 

 lutely the magnitude of a sound field without the use 

 of an electroacoustic transducer. Among these may 

 be listed the Rayleigh disk method, the radiation 

 pressure method, and optical methods. These all re- 

 quire relatively delicate measurements which, while 

 difficult to perform in air, are even more difficult in 



