11-13 



of scattering inhomogeneities in this disk will therefore be proportional to 



2 4 . The power scattered by the disk will again be the sum of the power 



scattered by the individual scatterers in the disk which, using (II- 4) for the in- 

 dividual scatterer, yields: 



power scattered by disk ~ I 3 ^^4 1 I Jj. I = IvpR^k^ (II-7) 



There are again -r^ disks, and the total coefficient of variation (the square root 

 2K 



of the power ratio) therefore becomes: 



L 



V --d ^ |v| Rk~|v| k^^TT (II-8) 



We observe that the coefficient of variation is again proportional to the square 

 root of the range, but that the dependence on the frequency of the incoming sound 

 and the size of the scatterer is quite different from that in the low frequency case. 



Finally, we turn to the near (focusing) range for high frequency scat- 

 tering. The physical situation is depicted in Figure II- 5. The scattered pressure 



L 



received by an observer is now due to a portion of each of — single scatterers 



lined up in a row. Only part of the total volume of each of the scatterers con- 

 tributes to the sound received by the observer. In fact, the contributing scatter- 

 ing volume for a scatterer a distance L from the observer is now given by: 



-ur 



T (L) - 2R { — ) ~ ^J^ (II-9) 



The power received by the observer is again the sum of the individual scattered 

 powers from these portions of the single file of scatterers; therefore, the coef- 

 ficient of variation becomes: 



V .JX /iiT(Ly^\ lV^IvI 



p ^2R ^ L j rV2 



Inside the focusing range, therefore, the scattered power is independent of the fre- 

 quency of the incoming sound and increases as the three-halves power of the range. 

 This is the result that would be obtained by a ray- acoustics analysis for the stand- 

 ard deviation of the phase of the received signal. 



Arthur B.littleJnr. 



S-7 001-03 07 



