ESTABLISHMENT OF SOUND FIELDS 



63 



at the same terminals at which the current into the 

 transducer is measured when operating as a trans- 

 mitter. The choice of the terminals can be arbitrary 

 to a considerable extent. They may be directly at the 

 electric output of the transducer element itself (for 

 example, the crystal, in a transducer of that type) or 

 at the end of a considerable length of cable. In fact, 

 two terminals of a four-terminal passive electric net- 

 work may be connected to the transducer, and the 

 terminals used in the calibration selected as the re- 

 maining pair of terminals of the network. Any of 

 these conditions is satisfactory, provided the same 

 pair of terminals is used for both current and open- 

 circuit voltage measurement. 



2. It is specified above that the distance d should 

 be large enough so that waves from either the pro- 

 jector P or transducer T (when transmitting) are 

 effectively plane at this distance. This is necessary 

 if the plane wave calibration of the hydrophone H 

 is desired. The distance may be shortened if one 

 wishes to obtain a calibration for H in terms of 

 spherical waves of a given radius, or if one can apply 

 a spherical wave correction to reduce a spherical wave 

 calibration to a plane wave calibration. The latter 

 procedure may be necessary if reflection interference 

 is present to a degree which seriously interferes with 

 the accuracy of the measurements. The presence of 

 reflections introduces the same inaccuracies in a re- 

 ciprocity calibration as in comparison tests, and the 

 methods described in Section 5.3 for eliminating re- 

 flection interference may often be profitably applied 

 in reciprocity calibration tests. 



3. We have indicated that the choice of the acous- 

 tic center of the transducers was arbitrary in the pre- 

 ceding discussion, yet the distance d between centers 

 enters explicitly into the formula for the calibration. 

 This can be understood if one remembers that the 

 receiving response also depends upon the choice of 

 the center, and this latter dependence on d cancels 

 the explicit dependence on d in the formula. See 

 Chapter 4, equation (10). Usually the acoustic center 

 is chosen close to the geometric center of the instru- 

 ment, but in principle one may take it to be any- 

 where. If it should be chosen far from the actual 

 instrument, the center must be considered as part of 

 the instrument in requiring that the wave be essenti- 

 ally plane; that is, the plane wave response with such 

 a choice for the acoustic center can be obtained only 

 if the wave from the transmitters is essentially plane, 

 not only over the transducer but over the entire re- 



gion between the center and the transducer. Thus, 

 there is an advantage, insofar as choice of testing dis- 

 tance is concerned, in selecting the center within, or 

 in the immediate neighborhood of, the transducer. 



4. It should be clear that the reciprocity calibra- 

 tion of a transducer can be carried through for any 

 orientation (direction of sound incidence) of the 

 transducers involved, but the same relative orienta- 

 tions must be maintained during the series of tests. 

 One also sees immediately that the directivity pattern 

 of a transducer obeying reciprocity is the same on 

 transmitting and on receiving at the same frequency. 



5. One should note that the responses given by the 

 formula represent ratios of magnitudes of quantities 

 without consideration of phase. To obtain the phase 

 of the response, one must include a phase factor, 

 which is not ordinarily known but can be deter- 

 mined in the reciprocity relation shown in equation 

 (56) lor the particular reversible transducer. The 

 phase of the response is not usually of interest, but in 

 some cases it may be important. 



6. In making a reciprocity calibration one must 

 have a transducer obeying the reciprocity principle, 

 and therefore should have a means of establishing 

 this property. While it is known that it is possible to 

 have a linear passive reversible transducer which does 

 not obey reciprocity, almost all transducers of interest 

 do have this property. No generally applicable condi- 

 tions have been established to guarantee reciprocity 

 in a transducer, but there are some general principles 

 which serve as useful guides. Theory seems to indi- 

 cate that it the electromechanical coupling is of the 

 electromagnetic or magnetostrictive type, or a com- 

 bination of these, reciprocity is obeyed. Similarly, 

 there are indications that electrostatic or piezoelectric 

 coupling or a combination of these also insures reci- 

 procity. A parallel combination of one of the first 

 group (electromagnetic or magnetostrictive) with one 

 of the second (electrostatic of piezoelectric) in general 

 leads to a transducer which does not obey reciprocity. 

 Since such combinations are rare, most actual trans- 

 ducers will apparently obey reciprocity. The condi- 

 tion for reciprocity is sufficiently established if the 

 efficiency of the transducer is 100 per cent. Since no 

 actual transducers attain this efficiency, this criterion 

 is of questionable value for practical application. 



One must therefore resort to the criterion of in- 

 ternal consistency between the calibrations obtained 

 with several reversible transducers as a check that 

 they obey the reciprocity principle. It is very unlikely 



