TRANSDUCER HORIZONTAL 



307 



where iV is the number of bubbles per cubic centi- 

 meter, 0-, and (T, are respectively the absorption and 

 scattering cross sections of a resonant bubble (de- 

 fined in Chapter 28), D is the distance AX, a the 

 usual attenuation coefficient equal to about 4 db per 

 kyd, and r the range. 



Evaluating the integral in equation (29) of Chap- 

 ter 12 with the aid of equations (11) and (12), 

 and, comparing the result with equation (39) of 

 Chapter 12, it is readily found that 



-— sin 5 = 



2a e 2(7. r 



(13) 



where 6 is as usual the angle of elevation of the ray 

 from the projector to the scatterer at range r (Figure 

 7, Chapter 12),andd the projector depth. Foratrans- 

 ducer at 16 ft, equation (15) gives m' equal to —28 db 

 at 100 yd and -38 db at 1,000 yd (using Figure 1 

 in Chapter 34). These values are about 6 db lower 



than the median measured values of —22 db and 

 — 31 db and are still lower than the highest reported 

 levels at 100 and 1,000 yd (see Figure 31). Since equa- 

 tion (13), derived on the basis of a densely populated 

 surface layer, gives the highest possible value of m' 

 for scattering by bubbles, it seems that measured 

 surface reverberation levels cannot be explained on 

 the hypothesis of scattering by a surface layer of 

 bubbles. It will be noted that, because of the assumed 

 neglect of scattering along OBX (Figure 32), in 

 this situation of scattering by a densely popu- 

 lated surface layer of bubbles the value of m' indi- 

 cated by equation (13) is the true surface-scattering 

 coefficient. Thus, although the argument presented 

 in Section 12.5.6, that measured values of m' are 6 db 

 greater than the true value of the surface-scattering 

 coefficient, is probably valid, it is evident that the 

 vaUdity of this 6-db relation depends on the physical 

 process which gives rise to the surface reverberation. 



