966 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



or by 



K2U = 2{fjL + \)(x^ cos jS sin 



ax 



- (\^ + (2/x + X)«') cos OL sin ^ 



(lb) 



where Ki = (XjS'- + (2/1 + \)a^)K sin /3, 2^2=20* + \)a^K cos /8, at aU 

 points (a, jS) satisfying (3). Similarly from (2) and the boundary conditions, 

 the a;-dependence W of the displacement component along the slab will be 

 given by 



K^W = {\^ + (2/1 + \W) sin jS cos ~ - 2(/i + X)a/3 sin a cos — (2a) 



a a 



or by 



iTiTF = 2{tM^ - (2/x + X)a') cos i8 cos — 



+ (XjS" + (2/1 + X)a') cos a cos ^, 



a 



(2b) 



iTa = iana{)x + X) ^, "j^ |^|^ [j^ ^^^ K sin ^, 7^4 = 2ioaa{}x + X)2r cos /3. 



Examine now, for example, a material for which X = /i, in the branch 

 whose cut-off is at j9 = 27r, a = lir/y/lt. It can be verified at once that the 

 nodes of the two components at some of the values of (a, /3) discussed ear- 

 lier are described by the following table ( in which / = cos — 1 : 



It is to be noted in general that the nodal variations become less extreme 

 at high frequencies, since for all branches except the lowest V and W tend 



