TRVN.SM1.SSION WITH i\e<;ative <;k adients near surface 



127 



SURFACE 



P B = L 



.LIMITS OF ACTUAL SOUND BEAM 

 .LIMITS OF ASSUMED TILTED BEAM 



Figure 46. Diagram used in calculating scattered sound intensity. 



the scattered sound is transmitted to the entire ocean 

 as if refraction were not operating. Also, for the pur- 

 pose of calculating the sound scattered into the 

 shadow zone, the actual direct beam may be replaced 

 by a tilted beam traveling in a straight line, as in 

 Figure 46. 



To calculate the scattered soimd received when a 

 long (10-sec) pulse is sent out, it may be assumed 

 that sound scattered from the entire length of 

 the beam is received at the hydrophone. Let the total 

 initial power in the beam be denoted by /. If attenua- 

 tion is neglected, this energy will remain constant as 

 the sound travels outward. If the scattering coef- 

 ficient is m per yard, a fraction m of the sound energy 

 will be scattered per yard of travel of the beam (see 

 Chapter 2 of Part II). This energy will be scattered 

 in all directions; and the intensity of the sound scat- 

 tered from this cross section of the beam 1 yd thick 

 and reaching the hydrophone at a distance r' yd away 

 will be mJ/47rr'2. While in actual fact the sound 

 scattered from the lower side of the beam will be more 

 weakened than that scattered from the upper side, 

 the distance r' from the hydrophone to a point on the 

 axis of the beam should be a reasonable approxima- 

 tion for each separate cross section of the beam. Let I 

 represent the distance from the projector to the point 

 where scattering is taking place. The sound scattered 



between I and I + dl is thus {mJ/4:irr'^)dl; and the 

 total scattered sound received at the hydrophone is 



r " mJ mJ r " 



Jo 4irr'2 47r Jo 



dl 



(L - ly- + d' 



(17) 



where the quantities L and d have the meanings 

 shown in Figure 46. The integration yields approxi- 

 mately 



mj/ir\ mJ , ^ 



While in the general case m will be a complicated 

 function both of position in the ocean and of the 

 direction in which the scattered sound is measured, 

 here m is assumed to be constant. Equation (18) thus 

 refers in practice to an average value of m. 



The expression (17) does not take into account the 

 transmission anomaly resulting from absorption or 

 refraction. When a sound beam is refracted sharply 

 downward, the intensity in the direct sound field is 

 not reduced much below the inverse square value. 

 The scattered sound, which reaches the hydrophone 

 at steep angles, is also relatively unaffected by re- 

 fraction. The absorption must be considered, how- 

 ever. For points in the sound beam to the left of the 

 point B in Figure 46, the sum of the absorption loss 

 for direct and scattered sound will not depend much 



