6233 HYDROGRAPHIC MANUAL PaGE 572 



upper and lower depths of the layer through which linear velocity change per unit of 

 depth is assumed. The projection of the line on the abscissa scale of the curve gives the 

 range of velocity throughout this depth. With these data the lengths of the are paths 

 and the total horizontal distance can be computed. The earth's curvature is neglected 

 for the distances involved. A number of angles of emergence of sound are assumed 

 and the refracted paths are computed through each layer. All the arc distances are 

 summed and the projections of the arcs on the horizontal are likewise summed for each 

 initial angle assumed. Each angle will give a different total horizontal distance and arc 

 length. 



The formulas for makmg these computations through a single layer are given with 

 figure 127. The values required are R, the horizontal component of travel, and a, the 

 length of arc traversed by the sound. The radius of curvature of the sound path through 

 any layer is equal to the initial velocity Vi divided by the product of the velocity gradi- 

 ent within the layer and the sine of the incident angle. The angle ii is the incident 

 angle of the sound ray on entering the layer and from this the angle at which the sound 

 leaves the layer may be found from the formula: 



.^s.-.(|s.,> 



This is all that is necessary to calculate the horizontal distance R and the arc distance 

 a by the method indicated in figure 127. If ^7l is less than V2 the same method is used 

 except that the center of radius of curvature will lie above the layer. 



Where the sound path does not penetrate through the layer, the method of comput- 

 ing the distances is shown in figure 128. This illustrates a result commonly found in 

 deep water, where the refraction due to increasing velocity caused bj'' the increase in 

 hydrostatic pressure with depth, reverses the direction of propagation back toward 

 the surface (see 6222) . The total horizontal distance and the total distance along the 

 curved path traversed by the sound are found, if the depth of water can be assumed to 

 be composed of layers, by adding the distances for each layer through which the sound 

 passes. 



6233. Reduction of Sound Energy 



As discussed in 621 and 6224, the reduced sound energy at the point of reception 

 may be due to the following: spreading, absorption, reflection, refraction, diffusion, 

 diffraction, and interference. 



From a nondirective source, sound is propagated in all directions. The sound 

 intensity would decrease in proportion with the square of the distance from the source 

 if there were no other form of energy reduction. This reduction due solely to distance 

 is termed spreading and has been discussed in 6224. But it is known from observation 

 that the sound intensity decreases much more rapidly than this. 



Absorption may account for part of the additional loss. The absorption due to 

 viscosity and thermal conductivity is relatively small at the frequencies associated with 

 R.A.R. (see 656). Most of the absorption that takes place is because of gases in the 

 water. Gases in water may result from turbulent surface conditions or from the pres- 

 ence of marine life. Gases arc mostly found in the layers of water close to the surface. 

 Where the water is shoal, however, this layer may be a large percentage of the total 



