RECIPROCITY CALIBRATION OF STANDARDS 



145 



90* 



Figure 16. Measured directivity pattern of QIS No. I 1 1 

 transducer at 25 kc. Directivity index computed from iliis 

 pattern = —21.1 db. 



the projector efficiency. The only factor still unknown 

 in this expression is 10 log P, jP A . This expression can 

 be evaluated from the impedance of the projector and 

 the source impedance (see equation (2) in Chapter 4): 



10 log ^ = I01og[~ 7 — j-^f- — ; 1 



.„, \~4x8. 7x1351 

 = 101o -"L l43.7^+15(p J 



= -9.fi db. 



The efficiency can now be stated 



E v = 4-82.0-24.2 + 9.6-70.9= - 3.5 dbvs ideal. 



_-120 



£ -140 



Io00 CYCLES/SEC »° 



1000 

 100,000 



Figure 17. Reciprocity parameter for water. 



T 2dx "I 



7 = 20 log x lO" 1 . 



M RECIPROCITY CALIBRATION 



OF STANDARDS 



The comparison method of calibrating acoustic de- 

 vices depends on the availability of standards whose 

 calibration is accurately known. The next problem, 

 then, is to calibrate these standards. As discussed in 

 Chapter 5, the best method for obtaining an absolute 

 calibration is by means of the reciprocity principle, 

 which permits a determination of the response from 

 purely electrical measurements. The reciprocity cali- 

 bration requires considerably more work and is more 

 critical than a relative calibration. Therefore its use 

 should be confined to the fundamental calibration of 

 hydrophone standards, with which all other instru- 

 ments can then be compared. 



The relation by means of which the reciprocity cali- 

 bration of a hydrophone can be obtained is given in 

 Chapter 5. In decibel form this equation is 



R, = i/ 2 [,/ + 20 logo, + 20 log r ft ' 



- 20 log e t - 20 log*'] (5) 



where / = 20 log (2dX/ P r x 10" 7 ). The term / is the 

 reciprocity constant. This parameter for water for a 

 number of testing distances is shown in Figure 17. 

 The term c h is the open-circuit voltage generated by 

 the device in a given sound field, r, is the open-circuit 

 voltage generated by an auxiliary transducer in the 

 same sound field, and c h ' is the open-circuit voltage of 

 the device in the sound field produced by the auxil- 

 iary transducer when a current i flows through it. 



The data usually are furnished by the test station 

 in terms of level in db vs 10 lc watt rather than volt- 

 age. The matter of translating levels into db vs 1 volt 

 is discussed in Section 7.3. Since most of the circuits 

 used at the test stations have an impedance of 135 

 ohms, it is sufficient here to consider that case, in 

 which the correction is —138.7 db. The above equa- 

 tion can now be written in terms of levels: 



7?,. = i/ 2 [J + L„ + L„' - L, - 20 log i - 138.7]. (6) 



Usually the same transducer is used for the calibra- 

 tion of a number of hydrophones. Then the following 

 quantities, which are independent of the particular 

 hydrophone being calibrated, can be computed, and 

 the result used as a constant k in the other reciprocity 

 computations: 



k =J-L t -20 log/ - 138.7. 



(V) 



