52 



TESTING TECHNIQUE 



0.5 1 2 



Figure 12. Determination of testing depth. 



Equation (34) is plotted in Figure 12 for convenient 

 reference. In the above derivation it is assumed that 

 R b and R a are independent of the angle of incidence 

 and thus of d and h. However, since these reflection 

 coefficients do depend upon the angle of incidence, 

 and since their effective values depend also on the 

 directivity of the device being tested, equation (35) 

 should serve as a guide rather than as a rule in choos- 

 ing the testing depth. Usually a testing depth lying 

 between t/ 2 and y 4 of the water depth is satisfactory. 

 The more absorptive the bottom, the greater is the 

 relative testing depth which may be used. 



5.4.2 



Distance 



Choosing the optimum testing distance is even 

 more difficult than choosing the optimum depth, 

 since more considerations must enter into the deter- 

 mination of the former. If the testing distance is too 

 great, reflection interference becomes very promi- 

 nent, and when a low intensity source is used, diffi- 

 culties with ambient noise may arise. On the other 

 hand, if the distance is too short, proximity effects 

 due to the spherical wave front incident on the re- 

 ceiver introduce errors into the calibration, or a 

 standing wave diffraction pattern may be set up be- 

 tween transmitter and receiver. Thus, the selection 

 of the optimum distance must be made as a com- 

 promise between these competing effects. The de- 



pendence of surface reflections on testing distance 

 and depth has been discussed in considerable detail 

 in preceding sections of this chapter. Now it is neces- 

 sary to discuss the proximity effects in detail before a 

 criterion for the selection of testing distance can be 

 determined. Because of the reciprocity principle (see 

 Chapter 3 and Section 5.5.6), proximity effects for a 

 transducer are the same whether it is acting as a trans- 

 mitter or as a receiver. 



543 Proximity Effect for 



Pressure-Gradient Receivers 



A pressure-gradient or velocity-type hydrophone 

 is one whose response is (at least over a certain fre- 

 quency range) proportional either to the component 

 of the pressure gradient or to the particle velocity 

 of the sound field parallel to the axis of the hydro- 

 phone, rather than to the pressure in the sound field. 

 In a plane sound wave, the pressure gradient is pro- 

 portional to the pressure in the sound field, the 

 proportionality constant being independent of fre- 

 quency. For spherical waves this is not the case 

 except for sufficiently great distances from the center, 

 where the wave front is essentially plane over the 

 hydrophone. Since the calibration of pressure-gra- 

 dient hydrophones usually is desired in terms of the 

 equivalent plane wave pressure, it is then necessary 

 to employ a spherical wave correction. 



To obtain this correction, one uses the equation 

 for the pressure in a spherical wave at a distance r 

 from the center 



p,,e 



-jkr 



(36) 



where jt>„ is a constant, and />• = 2tt/\, A being the wave 

 length. The radial component of the pressure gradi- 

 ent is then given by 



dp _ (1 + jkr)e-*<- 



(37) 



The ratio of pressure gradient to pressure is therefore 

 given by 



(I) ( 



-p„(l +jkr)e 



-) 



(1 +jkr) 



(^~) 



(38) 



