168 



INTENSITY FLUCTUATIONS 



work has indicated, though, that the time rate of 

 fluctuation is range-dependent, that is, the time rate 

 decreases as the range increases, at least in the direct 

 sound field. In addition, observations made when the 



3 



99 



98 



97 



96 



95 

 94 

 93 

 92 

 91 

 90 



BO 



u 70 



60 



5 30 



•■ 40 



30 



eo 



10 



T I 1 



I 2 3 4 9 • 



Figure 8. Observed cumulative distribution suggest- 

 ing image interference fluctuation. 



roll of the transmitting ship was less than 2 degrees 

 show about the same fluctuation as other data. Thus, 

 while no definitive conclusions can be drawn at the 

 present time, it seems unlikely that roll and pitch are 

 dominant causes of the observed fluctuation in under- 

 water sound transmission. 



7.2.2 Interference 



If the sound signal received at the hydrophone 

 were the resultant of several individual signals trans- 

 mitted over two or more paths, any change in the 

 relative phases and amplitudes would cause a change 

 in received signal strength. If the properties of the 

 transmission paths were subject to random variations, 

 the resulting variability of the received signal would 

 depend on the characteristics of these variations. 



Several different models of underwater sound trans- 

 mission have been studied which involve multiple 

 paths of transmission. 



Two Paths 



We shall consider, first, interference between the 

 direct and the surface-reflected signal. If the geome- 

 try of one or the other path could be changed ran- 

 domly, the result should be a fluctuation in the rel- 

 ative amplitudes or, at least, in the relative phases of 

 the two interfering signals. 



Some evidence has been accumulated which indi- 

 cates that interference between the direct signal and 

 the surface-reflected signal is at least a major con- 

 tributing cause for the observed fluctuation. Figure 

 8 shows a distribution of amplitudes similar to sev- 

 eral which were observed at UCDWR. The theoreti- 

 cal curve corresponding to the expression (25) (with 

 «! equal to ir/A times the mean amplitude a) is super- 

 imposed on the observed points. The moderate agree- 

 ment indicates that during the run from which this 

 distribution of amplitudes was obtained, random in- 

 terference between two equally strong signals could 

 have been the principal cause of fluctuation. On the 

 other hand, a large number of observed amplitude 

 distributions fail to conform to the expression (25), 

 suggesting that the assumed mechanism is not al- 

 ways the principal cause of fluctuation or, at least, 

 that it is frequently modified by other mechanisms. 



Another argument in support of the hypothesis 

 that fluctuation is caused, in part, by interference be- 

 tween the direct and the surface-reflected signal is 

 provided by the absence of regular image interference 

 patterns for most transmission runs at supersonic 

 frequencies. While traces of the pattern are regularly 

 observed for transmission at low sonic frequencies 

 (see Section 5.2.1), they are almost never found be- 

 yond 100 yd at frequencies exceeding 20 kc. This 

 absence has usually been explained by the size of the 

 irregularities of the sea surface. While at very low 

 frequencies the wavelength of underwater sound is 

 large compared with most of the water waves, this is 

 not true for supersonic sound. Irregularities of the sea 

 surface may well replace the theoretical image inter- 

 ference pattern by an image fluctuation; this conjec- 

 ture is supported by the fact that fluctuation at sonic 

 frequencies is often markedly lower in magnitude 

 than it is at supersonic frequencies. A very striking 

 plot of a transmission run at 20 kc showing both 

 image effect and image fluctuation has been pub- 



