206 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



RANGE IN YARDS 

 800 1200 



1600 



SOUND VELOCITY 

 RELATIVE TO MAXIMUM 

 IN FEET PER SECOND 



2000 -40 



Figure 11. Velocity -depth curve and sample ray paths for Figure 10. 



The three oscillograms on the right of Figure 10 do 

 seem to show a regular trend, however, in that with 

 increasing range the first pulse becomes rapidly- 

 weaker in comparison with the second, and its time 

 of rise increases. Comparison with the oscillograms of 

 Figure 7, which show the same trends, suggests that 

 the first pulse may have reached the hydrophone by 

 diffraction, while the second corresponds to a direct 

 ray. The possibility of a phenomenon of this sort 

 is suggested by calculations which have been made 

 on ray paths for this day, a few of which are shown 

 in Figure 11. The ray ABC crosses the 100-ft depth 

 line at a greater value of the horizontal range than do 

 rays of slightly greater or slightly smaller inclina- 

 tions so that this ray and its neighbors have an en- 

 velope, or caustic, passing through B. This caustic 

 forms a shadow boundary as far as rays of inclina- 

 tions near that of ABC are concerned,'* although it 

 happens in this case that rays having considerably 

 greater inclinations fall outside the caustic. The com- 

 plete ray diagram would of course be quite compli- 

 cated, and attempts at a detailed correlation of the 

 oscillograms with the bathythermograph data have 

 not been very successful. 



The oscillograms shown in Figure 12 are for shots 

 made on the same day as those in Figure 7; bathy- 

 thermograph data and ray diagrams for this day have 

 been given in Figure 6. These oscillograms show that 

 even when no crossing of rays is predicted, multiple 

 peaks and similar irregularities can still occur, al- 

 though these features are less pronounced than in 

 Figure 10. As was cautioned in Section 9.1, instru- 



mental sources for such irregularities must always 

 be suspected; however, it seems likely that many of 

 the unexplained irregularities found in UCDWR ex- 

 periments are due in some way to oceanographic 

 conditions. 



9.2.4 Results of Fourier Analysis 



So far we have discussed the propagation of ex- 

 plosive sound with little mention of its relation to 

 sinusoidal sound waves. There is an important rela- 

 tion between the two, however. Any pulse of arbi- 

 trary shape can be approximated as' accurately as 

 desired by a linear superposition of a sufficiently large 

 number of sine waves, of suitably chosen frequencies, 

 amplitudes and phases. If the laws of propagation of 

 sound are linear in the amplitude of the disturbance, 

 as we believe them to be when the amplitude is suf- 

 ficiently small, we can predict the changes in the size 

 and shape of the pulse as it travels through the water 

 from the changes in amplitude and phase which each 

 of the sine waves would undergo if it were present by 

 itself. Conversely, if the behavior of the pulse were 

 accurately known, the attenuation and dispersion of 

 all the component sine waves could be calculated.* 



An analysis of this sort can be extremely useful in 



» That this is indeed a practical possibility has been demon- 

 strated in some experiments at NRL" in which the rela- 

 tive calibration curve of the two hydrophones was determined 

 over the range from 5 to 100 kc by Fourier analysis of their 

 responses to detonating caps. The resulting curve was found 

 to be in excellent agreement with one determined by standard 

 CW methods of calibration. 



