Page 563 radio acoustic ranging 6222 



For subaqueous sound ranging in very shoal water, where the ratio of the horizontal 

 distance to depth is 200 to 1, or greater, the actual lengths of the sound paths, where 

 few reflections are involved, differ very little from the respective horizontal distances. 

 Figure 123 is deceptive in this respect because the vertical scale is greatly enlarged and 

 does not show the true relation of depth to distance that exists in practice. In a depth 

 of 50 fathoms for a distance of 10 nautical miles, the path of a sound wave that has 

 been reflected 12 times is only 33 meters longer than the horizontal distance. For a 

 greater depth and longer distance, the difference will, of course, be larger — for example, 

 where the depth is 1,000 fathoms and the distance is 50 miles, the theoretical difference 

 between the path of a sound wave reflected 12 times and the true horizontal distance 

 is 2,550 meters. 



6222. Refraction of Sound 



Any change which i^ay occur in the direction of propagation of a sound wave is 

 obviously of primary importance in subaqueous sound ranging. A change of sufficient 

 magnitude in the direction makes the simple laws of reflection inapplicable, for if the 

 direction of propagation is changed sufficiently in a vertical plane toward the point of 

 reception, the number of reflections is altered, thus increasing or decreasing the length 

 of the reflected path. Unfortunately such a change in the direction of propagation of 

 sound does take place in all water media. This is known as refraction. Refraction of 

 sound makes any analytical study of the propagation of sound more difficult. Also it is 

 doubtless responsible for many of the difficulties that are experienced in subaqueous 

 sound ranging and hence a thorough understanding of its laws is necessary. 



The change in direction of a sound wave caused by refraction is shown in figure 

 124. Where any part, as ai, of the incident wave Wi in. the first medium encounters 

 the boundary between media at point a, it will be refracted from this point as a second- 

 ary source, or origin, at a different velocity. Succeeding points in the incident wave 

 will be refracted later at corresponding points along the boundary until the entire 

 wave penetrates the boundary and the refracted wave W2 is formed. It is evident from 

 the figure that the wave in the second medium will travel at a different angle owing to 

 the fact that the velocity in this medium is different. All the energy is transmitted 

 through the boundary only when the acoustic resistances of the two media are equal 

 and the angle of incidence is normal to the boundary. Where the acoustic resistances 

 of the two media are different, a varying amount of the energy will be reflected de- 

 pending on the difference in acoustic resistances and the angle of incidence. Where the 

 angle of incidence is greater than the critical angle, regardless of the relation of the 

 acoustic resistances, no transmission into the second medium takes place, and all of the 

 incident energy at this angle and greater is reflected (see 6221). 



Refraction occurs wherever a sound wave encounters either a boundary between 

 media in which the velocities of sound are different, or in a medium in which the velocity 

 of sound is continuously changing. If a sound wave in transmission encounters a 

 boundary between media in which the velocities of sound differ, the direction of propa- 

 gation will be changed. If the velocity of sound in the first medium is greater than it 

 is in the second medium the direction of propagation will be changed away from the 

 boundary between the media, as in figure 124, but if conditions are reversed and the 

 velocity in the first medium is less than in the second, the change in the direction of 

 propagation will be toward the boundary. The angular change in the direction of 

 propagation may be found from the formula given with figure 124, in which i'l is the 

 angle of incidence in the first medium and 2*2 is the angle of refraction in the second 



