III-28 



The intensities of the incident and scattered sound are given by (see 

 Equation III- 6): 



I 13 I IS 



, _ I mc I -. I sc I 



inc 2p^c^ sc 2p^c^r = 



and the total scattered energy at the distance r is 4nr^ Ig^,. The scattering 

 cross section Oqq is defined by the expression 



ivr"! = o I. 



sc sc mc 



that is, it is the area such that the total incident energy crossing this area in a 

 perpendicular direction is equal to the scattered energy. Then o is given by 



4tt p 

 sc 

 o ' - — r-2- 



sc p. 



inc 



The scattering cross section does not provide all the information wanted in the 

 case of an actual bubble, since the incident energy is reduced by both scattering 

 and absorption. Let F be the sum of these energies, i.e., the total energy 

 extinguished from the incident wave. Then an extinction cross section can be 

 defined analogously by 



o I. = F 



ex inc ex 



The quantity Fg^^ is equal to the work done, per unit interval of time, on the 

 bubble by the incident sound beam. Then, for a bubble of radius a, we have 



F = (Rep. (t)) (4na^) (Re --) 

 ex inc dt 



:3[rtbur Sl.littleJnt. 



S-7001-0307 



