the wedge angle and incident wave angle, subregions II and III may not exist 

 at all. In general, the solution function can be written as 



= * (r,8) + *(r,6) 



(11) 



where 



(r,6) = 



it - a > e > 

 Tr + a>6>ir-a 

 > 6 > tt + a 



(12) 



The equation reveals that <j> is the sum of the incident and reflected waves 



<f>, and 4> and is a known function. The scattered wave <t> is the only un- 

 T i r s 



known function to be determined in the problem. Nevertheless, the total wave 

 <j) instead of the scattered wave <j> is the desired solution to be obtained 

 in this study. 



12. The solution for the total wave <J> is pursued. The finite cosine 

 transform of $ , denoted by <$> , is introduced by the formula 



<Kkr 



VTl 



)(kr,6) cos ^ dt 



(13) 



where n = 0,1,2,... are integers, and v is related to the wedge angle as 

 defined by 



= vtt (14) 



o 



Applying the finite cosine transform and using the boundary condition in Equa- 

 tion 5, Equation 2 becomes 



2 8 2 <j> , 9<J) , 



r — £ + r -r 1 - + 



5 2 Sr 

 9r 



<« 2 - (?y 



= 



(15) 



Equation 15 is a form of the Bessel equation for which general solutions are 



the Bessel functions of the first and second kinds, J , (kr) and Y , ,(kr) , 



n/v n/v 



respectively. Since Y , (kr) are singular at the origin, the solution is 

 chosen to be 



