50 



TESTING TECHNIQUE 



^(f) {DECIBELS) 



Figure 10. Chart for obtaining correct level from differ- 

 ence in level between interference maxima and minima. 



The first term is measured directly and the second 

 calculated from the ratio determined above. The true 

 level for the frequency at any maximum is then the 

 measured value minus a determinable correction. By 

 a similar procedure, the correction to be added to the 

 measurement at a minimum is 



+ 20 log 



1 



D(f)J 



(31) 



These corrections are most readily made from the 

 curves of Figure 10 where the subtractive term from 

 (30) and the additive (31) are plotted against <£(/). 

 Thus, after constructing the maxima-minima differ- 

 ence plot, one need only take the value of <£(/) corre- 

 sponding to the frequency of each maximum and, on 

 going to Figure 10, read the number of decibels to be 

 subtracted from the maximum to give the correct 

 level. A similar process gives the number of decibels 

 which should be added to a minimum to find the cor- 

 rect level. 



While the above method is very useful in many 

 cases, it is not too satisfactory at low frequencies, since 

 it is difficult then to locate unambiguously the maxi- 

 ma and minima. There is no reasonably good method 

 for correcting for reflections at low frequencies. One 

 method may be of some aid, if only surface reflections 

 are prominent and both the source and receiver are 

 nondirectional. It is based on the fact that under 

 these conditions one can actually calculate the ob- 

 served pressure at the receiver in terms of the pressure 

 which would be present if the reflecting surface were 

 not present. This procedure can be carried through 



by following the instructions given with the nomo- 

 graphical chart, Figure 1 1. This method is useful for 

 calibrating very low frequency projectors. 



In the calibration of receivers by the comparison 

 method, the problem is somewhat simplified if the re- 

 ceiver under test and the one serving as a reference 

 standard are either both nondirectional (pressure- 

 activated) or both pressure gradient, since in this case 

 the reference field, even though it contains reflec- 

 tions, is the same for both instruments, and their rela- 

 tive calibration is correct in spite of the presence of 

 reflections.'' 1 



5-i CHOICE OF TESTING GEOMETRY 



541 Depth 



The testing geometry for a calibration test refers to 

 the testing depth and distance used. The optimum 

 depth is usually determined by the testing site so that 

 in general it remains the same during most tests. This 

 depth is limited by the available water depth and, as 

 a rule, its optimum value is that for which the magni- 

 tude of reflections from the surface is equal to that of 

 those from the bottom. If R s and R b are the effective 

 pressure reflection coefficients for the surface and the 

 bottom respectively, /;„. the depth of the water, h the 

 testing depth, and d the testing distance, ttten the in- 

 tensity of the reflected wave from the surface to the 

 receiver is 



R. 2 I a dT- 

 d> + 4h 2 ' 



(32) 



where /„ is the intensity of the direct wave. The in- 

 tensity of the reflected wave from the bottom is 



/?„-■/„ rf-' 



(33) 



Placing these equal to express the desired condition 

 and solving, gives 



(34) 



(35) 



R, 



