ESTABLISHMENT OF SOUND FIELDS 



59 



nel intimately familiar with every phase of the de- 

 sign. 



5. The reliability of calibration obtained in this 

 way is always open to question, unless a (heck can 

 be obtained by other methods. 



6. The frequency range which may be covered is 

 limited. 



One must conclude, consequently, that this is not 

 a very satisfactory method of absolute calibration, 

 although its principles are essential to the design of 

 satisfactory reference standards. 



5.5.3 Absolute Calibration from 



Calibration in Air 



Initially, the technique of calibration of acoustic 

 devices in air was developed considerably beyond 

 that in water. If one could obtain the calibration of 

 a device in water from its calibration in air, one 

 would have a useful method of calibration for under- 

 water sound devices. The mechanical and electrical 

 elements of a transducer are not functions of the 

 medium in which it is immersed. Therefore, it is 

 necessary to consider only the effect of a change of 

 medium on the acoustic elements. The important 

 parameters are the density and the sound velocity. If 

 a device is essentially pressure-actuated, the voltage 

 which it develops in a sound field is proportional to 

 the pressure properly integrated over its surface, in- 

 cluding the pressure due to diffraction. At wave 

 lengths where diffraction is negligible for a stiff' 1 de- 

 vice, the pressure acting is simply the pressure in the 

 field, so that the acoustic pressure is the same regard- 

 less of the medium. Thus, at low frequencies a stiff 

 pressure-actuated transducer has the same receiving 

 response in air and in water. The upper frequency 

 limit for this equality is determined by the frequency 

 at which diffraction becomes important. This fre- 

 quency is 14 to y r> as high in air as in water because 

 of the 4.3 to 1 ratio of the velocities of sound in the 

 two media. For a device of the order of 1 inch in size, 

 the frequency at which diffraction becomes important 

 is about 12 kc in air and about GO kc in water. Thus, 

 for a pressure-operated device of this type, such as the 

 3A hydrophone, a water calibration up to about 10 

 kc can be obtained from an air calibration, and, bv 



J By "stiff" is meant that, at the frequencies of interest, the 

 radiation impedance is small compared to the mechanical im- 

 pedance of the transducer. 



a judicious frequency translation of diffraction effect, 

 the calibration may often be extended higher. 



For a pressure-gradient operated instrument, the 

 response is essentially proportional to the pressure 

 gradient in the sound field. Now, for the same fre- 

 quency and pressure in a plane wave in air and in 

 water, the ratio of the pressure gradient in air to that 

 in water is equal to the ratio of the sound velocity 

 in water to that in air. If this were the only effect, a 

 pressure-gradient transducer would be 20 log 4800/ 

 1 100 = 12.7 db more sensitive in air than in water at 

 the same frequency. However, in such devices the 

 change in radiation impedance with change of me- 

 dium is often not negligible. The radiation reactance 

 of the transducer is a function of the density of the 

 medium, and the functional dependence is different 

 for different instruments. This effect must also be 

 taken into account. For the 1 A hydrophone, the addi- 

 tional correction amounts to 3.3 db, making the 

 hydrophone 16 db less sensitive in water than in air 

 at the same frequency. In addition, diffraction effects 

 become a factor in the response at different fre- 

 quencies for the two media, as pointed out above for 

 pressure-type instruments. 



Thus, a calibration in air 1 '- 4 can be used to give a 

 calibration in water only over a limited frequency 

 range. The original calibrations of USRL standards 

 before the reciprocity method was adopted were ob- 

 tained in this fashion. 



While, with judicious treatment of the data, these 

 methods can give reasonably good calibrations over 

 the most important part of the frequency spectrum 

 for underwater sound work, they have distinct dis- 

 advantages: 



1. They are relatively laborious and require for 

 their proper execution intimate knowledge of the 

 instrument, as well as personnel highly skilled in the 

 technique of air calibration and in the principles of 

 acoustic design. 



2. They can be applied only to relatively few in- 

 struments which are designed with this method of 

 calibration in view. 



3. There is no check on their reliability and no 

 positive assurance that the various modes of vibra- 

 tion of the device may not be excited to different de- 

 grees in air and in water. 



4. Theoretical corrections, whose validitv may be 

 questionable, must be applied to the results. 



5. The frequency range which may be covered is 

 limited. 



