and 



icod-if,) u + g |^= . (A-28) 



D oX 



From equation CA-28) we obtain 



u = - ■ , g. , ^ , (A-29) 



iaj(l-if, J 3x 



which may be substituted into equation CA-27) to yield the governing 

 equation : 



^2 gh b 

 8x ^ o 



which simplifies to the usual wave equation for f, equal to zero. 

 The general solution of equation (A-30) is given by 



-ikx +ikx ^. ^1-, 



? = a e + a_e , (A-31J 



in which a and a_ are complex amplitudes, whose magnitudes give the 

 physical wave amplitude, and k is the complex wave number defined by 



^ o 

 which may be written in terms of the usual wave number, 



k = -^^— (A-333 



rrr' 



(A-34) 



and 



/ 





e 





/-.^ 



k = k /Tif, = 

 b 



where 









tan2(i)^ = f^ 

 b b 









CA-35) 



Taking, for example, the wave solution of amplitude a in 

 equation (A-31), this reads: 



