Page 571 



RADIO, ACOUSTIC RANGING 



6232 



r cos 1 2 ■ 



Figure 127.— Path ol sound through a layer with uniform velocity decrease 

 from !'i to »2. 



From a point source, the sound energ;y' travels away in all directions at equal 

 intensity. The sound wave can therefore enter these layers, where the velocity gradient 

 differs, at a multitude of angles. The incident angle is the angle between the sound 

 path and the normal to the 

 layer boundary. The curva- 

 ture of the sound path in each 

 layer will be the same for each 

 angle but the lengths of the 

 arcs between the layer bound- 

 aries will be different. Where 

 the sound enters a layer at a 

 large incident angle, the length 

 of the arc in the layer will be 

 longer than where this angle is 

 small. For each angle of propa- 

 gation from the source, assum- 

 ing an infinite depth of water 

 and no loss of energy, the sound 

 will be refracted back to the 

 water surface, except for the 

 ray of sound propagated ver- 

 tically downward. , In such a 

 hypothetical case, that part 

 of the energy propagated most nearly downward, without being precisely vertical, will 

 travel the longest horizontal distance before striking the surface of the water. 



The path of refracted sound through the water for any shape of velocity-depth 

 curve, can be predicted by making certain allowable assumptions. Where the velocity 

 as a function of depth is known, it can be plotted as in figure 126. For the purpose, it 

 is assumed that the velocity-depth curve is the same throughout the region to be 



considered. This curve is 

 '^^ then divided into segments, 



each of which can be repre- 

 sented as a straight line 

 whose slope is the average 

 slope of that segment of the 

 curve. Theoretically an in- 

 finite number of straight lines 

 of infinitesimal length would 

 have to be used. However, 

 it has been foimd that a fair 

 degree of accuracy can be 

 obtained by dividing the 

 curve into a limited number 

 of straight lines depending 

 on the character of the curve. At least five lines should be used for a curve having an 

 irregular shape, but for a curve of regular shape a lesser number may suffice. The ends 

 of one of these lines projected horizontally onto the ordinate scale of the curve give the 



Figure 128.— Path of sound caused by a velocity increasing imiformly with depth 

 sufficient to refract the sound wave back toward the surface. 



