1190 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1952 



< 



<v -. 



:^® t* 



20 



50 

 C 



70 



Fig. 24 — Real and imaginarj' parts of Aj/tt^ and Aj/tt^ for a nonuniform stack 

 \vhose average properties are constant except at a single, unsymmetric discon- 

 tinuity. 



(1 



- y^ L T (1 - 



^o)Cj 



+ *■ 



C 



47r- 



L2(i - ^0) (1 - k^Y 



/o^ 



^o)Cj 



(550) 



Numerical values of Ai were found for the case ^o = I on the analog 

 computer and refined afterward by desk computation. The real and 

 imaginary parts of Ai/x" are plotted over the range ^ C ^ 100 in 

 Fig. 25, and the corresponding eigenfunction Wi{^) = Wi(^) + ivi{^) is 

 shoAvn in Fig. 26 for C = 0, 20, and 100. 



e^ 



10 20 30 40 50 60 70 80 90 100 



c 



Fig. 25 — Real and imaginary parts of Ai/tt^ for a nonuniform stack whose 

 average properties varj^ as a symmetric rectangular step. 



