TRANSMISSION IN ISOTHERMAL WATER 



95 



plete acoustic information is available, a modification 

 of the code system, more closely related to the typical 

 structure of the thermocline, will prove desirable. 



5.2 TRANSMISSION IN 



ISOTHERMAL WATER 



When temperature and salinity gradients are ab- 

 sent, the transmission of sound may be expected to be 

 relatively simple. If pressure did not affect sound 

 velocity, sound would travel outward in straight 

 lines, and the inverse square law of intensity decay 

 would be directly applicable. Since the effect of pres- 

 sure on sound velocity is in fact very small, one may 

 expect straight-line propagation to provide a reason- 

 ably good first approximation to the actual situation. 

 An examination of the ray diagram given in Figure 23 

 of Chapter 3 shows that the ray leaving horizontally 

 from a projector 15 ft deep in isothermal water is not 

 bent up to the surface until it reaches a range of about 

 1,000 yd. On the other hand, .'n an isothermal layer 

 100 ft thick the range to the shadow boundary is al- 

 ways greater than 2,200 yd. Thus, one may expect 

 that, certainly for ranges less than 1,000 yd and prob- 

 ably also for ranges up to 2,000 yd, the assumption 

 that sound travels in straight lines in isothermal 

 water is legitimate. This expectation is justified by 

 the observations. It will be shown later that the as- 

 sumption of straight-line propagation agrees with 

 some of the data out to very much greater ranges 

 than might be expected. The reason for this is not 

 known. In the following discussion, sound transmis- 

 sion measurements in an isothermal surface layer of 

 the ocean will, therefore, be discussed as though the 

 sound rays did, in fact, travel in straight lines in 

 such a layer. 



Even with all sound rays traveling in straight 

 lines, two influences act to disturb the ideal inverse 

 square law discussed in Chapter 2. In the first place, 

 sound is reflected from the sea surface; in the second 

 place, various impurities, and possibly also the water 

 itself, absorb energy passing through the sea, convert- 

 ing this energy to heat. The effects of surface reflec- 

 tion and absorption on the transmission of sound are 

 discussed later. 



5.2.1 Image Eifect 



It was shown in Section 2.6.3 that sound reflected 

 from the surface can reduce the sound intensity close 

 to the surface to a very small value. This effect arises 

 from the phase reversal suffered by a wave when it is 



reflected at a free surface. If pi is the pressure ampli- 

 tude at 1 yd from the .source, and if hi and h^ are the 

 depths of source and receiver respectively, we see 

 from equation (129) of Chapter 2 that the pressure 

 amplitude at the range R is given by 



Amplitude = — .sm 2w 



^ R RX 



If the simple inverse square law for intensity were 

 satisfied, the pressure amplitude at the range R 

 would be proportional to 1/R, that is. 



Amplitude = — • 

 R 



The transmission anomaly, which is the transmission 

 loss in decibels above that predicted by the inverse 

 square law for intensity, is therefore given by 



2 sin 2ir-^ ■ 

 R\J 



(2) 



If the surface is assumed to reflect only a fraction 

 fa of the sound energy incident on it, the analysis in 

 Section 2.6.3 must be modified. With a little mathe- 

 matical manipulation, the transmission anomaly for 

 this case becomes 



^ = - 10 log 1 - 2ya cos 4 





(3) 



The transmission anomalies resulting from this for- 

 mula for different values of ja are plotted in Figure 

 10. 



This analysis is of doubtful validity for short wave- 

 lengths since neglect of the surface water waves in 

 heavy seas is probably not legitimate for sound waves 

 only a few inches long. With calm seas, however, the 

 interference patterns predicted by the above analysis 

 have occasionally been observed at 24 kc at close 

 ranges. Equation (3) must be used with caution for 

 ranges much greater than 1,000 yd. The upward re- 

 fraction caused by the pressure effect, as well as the 

 variation in travel time caused by thermal micro- 

 structure, distort and obscure the interference pat- 

 tern predicted by the elementary theory. However, 

 the exact limits of validity of equations (2) and (3) 

 must be determined empirically. 



The available data show that for sufficiently low 

 frequencies, equation (2), or equation (3) with an 

 amplitude reflection coefficient ja nearly equal to 

 unity, provides an approximate description of the ob- 

 served transmission. In particular, beyond a range 

 R', corresponding to a path difference of a half wave- 

 length, the transmission anomaly increases steadily 



