as (8.25)., and then to see in each particular case what behavior oust 

 hold near the edge and what freedom exists for minimizing singular 

 behavior (as we shall do in $9). In some cases, in particular in recent 

 work by Rawlins [15] en diffraction of an acoustic wave by a half-plane 

 which is "sound-hard" on one side and "sound-absorbing" on the other, 

 the edge conditions are not at all obvious, being in fact 



l 

 4> - 0(x T ) 



3 



v<(> - 0(x~ T ) 



To justify acceptance of a solution with certain edge conditions 

 one has to go beyond the simple linear inviscid wave equation used here, 

 or beyond the simple zero thickness model of the boundary. For example, 

 one can look at linear acoustic propagation with viscous effects 

 included, or one can look at inviscid propagation around a surface which 

 is thin compared with any other relevant length scale but which has a 

 smoothly rounded edge. Il can be proven (though the proof has not yet 

 been published) that our solution with conditions (8.27) is the unique 

 one which can be matched to an "inner solution" in which either viscous 

 forces or the continuous curvature of the boundary lead to finite 

 velocities everywhere. That is a rather special kind of proof, however, 

 and we shall refer in $9 to the unavailability of a comparable proof 

 when there is uniform subsonic flow past the radiating half-plane. 



This discussion of edge-conditions completes the formal determina- 

 tion of the field as 



iv exp(-isx -Y y) 



211 L^a K - ( " q) (S + q)( ° " 



_ , ds (8.28) 



c q 



60 



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