6221 HYDROGRAPHIC MANUAL PaGE 562 



of any two given media, for different angles of incidence different relative amounts 

 of energy will be reflected, with one exception. The exception to this is found in the 

 specific instance of a source located in the medium of lesser sound velocity and where 

 the angle of incidence is equal to or greater than the critical angle. In this case total 

 reflection will take place. The critical angle of incidence of a sound wave is defined 

 as the angle, measured from the normal to the interface or bounding surface, whose 

 sine is equal to the ratio of velocity in the medium containing the source to the velocity 

 in the reflecting material, or medium. 



Therefore where the reflecting medium is air and the transmitting medium is 

 water there is no critical angle because in this case the ratio of velocities is greater than 

 unity. But where reflections from the ocean bottom are considered there will be a 

 critical angle. Where the angle of incidence is equal to or greater than this critical 

 value there will be total reflection, and where the incident angle is less than this critical 



Figure 123. — Multiple reflections in a bounded medium. 



value the reflection will be only partial. The critical angle of reflection from a bottom 

 of solid rock is about 17° but for other materials it may be as large as 70°. 



Hence in subaqueous sound ranging the critical angle will be approached only where 

 the horizontal distance between the source and the point of reception is less than six 

 times the depth of water (assuming the ocean bottom as flat and a critical angle of 70°) 

 and, therefore, total reflection from the bottom will occur at this and greater distances. 

 Furthermore, although theoretically total reflection will never occur at any angle at the 

 surface of the water, practically the amount of energy that is transmitted into the air 

 will be negligible due to the great disparity in the two radiation resistances. Thus in 

 practice total reflection may be assumed at both surfaces in nearly every case. 



From the source to a point of reception, sound may be considered theoretically 

 to travel along a number of reflected paths, one series which is first reflected from the 

 surface, and another series which is first reflected from the bottom, as in figure 123, 

 where, for clarity, only four of the paths reflected from each of the surfaces are illus- 

 trated. 



The first reflected sound that reaches the point of reception, where the source and 

 the point of reception are near the surface of the water, will have been reflected from 

 the surface at the point v, while the first sound reflected from the bottom to reach the 

 point of reception will be from point e. The second surface-reflected ray to be received 

 is reflected from the surface at point t and from the bottom at point /, while the second 

 bottom-reflected ray is reflected from the bottom at point d and from the surface at 

 point X. With a greater number of reflections the points of first reflections from the 

 surface and the bottom will be closer to the source. 



