Ill -67 



- Scattering cross sections are small enough to neglect 

 multiple scattering. 



- The average reverberation intensity at the receiver is 

 equal to the sum of the average intensities due to in- 

 dividual scatterers. 



- The backward scattering coefficient is independent of 

 the direction of incidence of the beam. 



In general, one must solve or invert (III-41) to determine volume scattering co- 

 efficients from measured reverberation intensities. 



Reverberation of a sinusoidal wave train radiated from a "search light" or 

 piston-type transducer (i.e., ma directional source having one radiation lobe, the 

 main lobe, much stronger than all others) and received by the same transducer has 

 been analyzed byUCDWR(Ref.III-39). The directional radiating and receiving proper- 

 ties of the transducer are considered to be identical, that is, F(t, 9, cp) can be written 

 F (t) b (9 cp). Assuming a sinusoidal pulse of the form p sin uu t , we then have 



p^ sln^ 2TT(fT-rA) 

 F(T, 8, cp) = -^ — 10* (III-42) 



where p is the instantaneous pressure in dynes/cm^ at a range r = 1 meter. 

 Assuming the transducer has axial symmetry, we have b(9, cp) - b(9). If m is 

 assumed to be independent of position 



I(t) = ^^ ' ^°* r-^- r m I b^(e)de (III-43) 



ct 



2p c 



I 



Using the experimental data, this equation was solved for m to give peak values 

 close to 3 • 10 at depths of about 400m in the frequency range 10-80 kc. 



Machlup (Ref. Ill- 15) has treated the problem of back scattering of the 

 omnidirectional shock wave from a nearby explosion to both omnidirectional and 

 searchlight receivers. Let F(t) represent the energy flux of the shock wave per 

 unit solid angle. Assuming t < < t so that r pa ct/2, the r integration can be 

 performed. The total energy in the shock wave can be written as 



"/ 



E = 4tt I F(T) dT (III- 44) 



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