96 



DEEP-WATER TRANSMISSION 



Figure 10. Theoretical transmission anomalies for different values of the reileetion coefficient of the surface. 



from its minimum value and, beyond a range of about 

 2R', increases equally with 20 log R. This range R' is 

 given by the equation 



4,hih2 



R' 



(4) 



More specifically, equation (2) is applicable for 

 frequencies of less than 200 c. For this low frequency, 

 this equation may be used out to ranges of 1,000 to 

 2,000 yd, beyond which bottom-reflected sound, even 

 in 2,000 fathoms, is usually stronger than the direct 

 sound. At 600 c the correspondence between theory 

 and observation is not so good, although the general 

 tendency predicted by equation (3) is definitely 

 present; possibly the best value of To for 600-c sound 

 is around }'2 to ^i. At frequencies greater than several 

 thousand cycles, no definite trace of image effect has 

 been consistently observed in the open sea. 



One of the earliest sources of observational infor- 

 mation on this subject consisted of a set of transmis- 

 sion runs made jointly in 1943 by the Columbia Uni- 

 versity Division of War Research at the U. S. Navy 

 Underwater Sound Laboratory, New London 

 [CUDWR-NLL], University of California Division 

 of War Research [UCDWR], and Massachusetts 

 Institute of Technology Underwater Soimd Labora- 



tory [MIT-USL]. ^~''' An acoustic minesweeper was 

 used as the source, and the signal was received with 

 band-pass filters centered at different frequencies. 

 The water depth was 600 fathoms. Unfortxmately, 

 the temperature near the surface was not isothermal 

 to 100 ft; in fact, in some of the runs sharp negative 

 gradients extended to the surface, and for some runs 

 the hydrophone was below a sharp thermocline. Since 

 the image effect was shown consistently at 250 and 

 700 c at ranges between 100 and, 300 yd, where bend- 

 ing by temperature gradients rarely affects measured 

 sound intensities, the data may be taken as an indica- 

 tion that the same effects would also appear in 

 isothermal water. 



Some transmission runs at 2 kc and at 8 kc also 

 showed some leveling off of the transmission anomaly 

 at higher ranges.* However, the steeper slope was 

 never so marked at ranges less than 500 yd that it 

 could be attributed to image effect rather than to 

 downward refraction. 



A detailed comparison between theory and obser- 

 vation for the sound of lower frequencies is made in 

 reference 10. Thetheorytakes bottom-reflected sound 

 into consideration and achieves rather good agree- 

 ment with the observational data. However, the 

 bottom-reflected sound comes in at such close range 



