36 



TESTING TECHNIQUE 



rotationally symmetrical about the Z axis, however, 

 only the pattern for lines in one plane (the XZ plane, 

 for example) need be given. When this symmetry does 

 not exist, measurements of the patterns in a few 

 planes are usually sufficient for practical applications. 

 It may be noted from the definition that the direc- 

 tivity pattern may be obtained for both hydrophones 

 and transmitters. For linear passive transducers which 

 obey the reciprocity principle, the directivity pat- 

 terns for the transducer in receiving and in transmit- 

 ting are identical (see No. 4 in Section 5.5.7). 



Impedance 



The impedance of a transducer is defined as the 

 complex (vector) ratio of the voltage across the ter- 

 minals to the current into the transducer. (See Chap- 

 ter 4.) The impedance depends upon the acoustic 

 termination of the transducer, and in principle the 

 impedance should be measured when the transducer 

 is in an infinite medium— water, in particular. 



5.1.3 



Ideal Testing Conditions 



An examination of the preceding definitions indi- 

 cates that, in order to measure properly the quantities 

 discussed in strict accordance with their definitions, 

 one must have (1) an infinite homogeneous medium 

 in which to perform the tests, (2) a source of plane 

 waves, and (3) no extraneous acoustic signals (am- 

 bient noise). While these ideal testing conditions are 

 impossible to meet in actual practice, they provide, 

 nevertheless, a useful standard with which to gauge 

 and appraise actual testing conditions. 



5 - 1A Compromises in Actual Testing 

 Conditions 



Testing Media 



It is evident that no infinite homogeneous testing 

 medium actually exists. If available bodies of water 

 are considered, two departures from ideal conditions 

 occur. Actual bodies of water are bounded by an air- 

 water interface at the surface and by bottoms ranging 

 in character from soft mud to rock. The influence of 

 these boundaries on a calibration test lies in the fact 

 that they reflect sound from the source so that the 

 acoustic signal reaching a measuring instrument con- 

 sists of the vector sum of the desired acoustic signal 

 and these reflections. Depending on the relative phase 

 and magnitude of these reflections, the measured 



Figure I. Coordinate system for transducer. 



signal magnitude may be greater or less than the 

 acoustic signal which one desires to measure. 



The obvious method of eliminating these effects 

 would be to choose a site in which bounding surfaces 

 are so distant from the testing locale that reflected 

 signals would be negligible compared to the desired 

 signal. Although this is a feasible compromise, there 

 are limits dictated by other circumstances as to how 

 far one can go in this direction. One of these, repre- 

 senting the second departure from ideal conditions in 

 actual media, is the lack of acoustical homogeneity of 

 available bodies of water over large distances. These 

 inhomogeneities are most often due to temperature 

 gradients in the medium, although other effects, such 

 as variations of salinity and increase of hydrostatic 

 pressure with depth, are sometimes significant. The 

 effect of these is to cause refraction of the acoustic 

 signal, thus disturbing the desired acoustic geometry 

 of the test and in general introducing unknown fac- 

 tors which influence the measurements. 



Plane Waves 



The only means by which one can generate truly 

 plane waves in an infinite medium is by means of an 

 infinite plane radiator. However, at sufficiently large 

 distances in a homogeneous medium, all sound gen- 

 erators of finite size produce waves for which the sur- 

 faces of constant phase are concentric spheres. If the 

 amplitude of the waves does not change appreciably 

 over the volume occupied by the device being tested, 

 and if the radius of the spheres of constant phase at 

 the test position is sufficiently large compared to the 

 dimensions of the device, then for all practical pur- 

 poses the wave field in the region may be considered 

 as plane. The greater the testing distance, the more 



