Now if p - on the six planes x^ - 0, l^, then it is required 

 that 



sinh vlr . = 



sinh(i|j.<E,. +i|f .) - 



b 



for £ = 1, 2, 3. This in turn yields ooj = and 



it follows that (45) will be valid only if 



(55) 



h i =n t {nll i ) (56) 



where n^ = 0, I, 2, . . . ; at least one of the n^ differs from 

 zero for non-trivial solutions. The relation for the wave 

 numbers and eigenfrequencies are thus formally the same 

 as before. 



It is possible, of course, to have a mixed boundary 

 condition for which the displacement vanishes on some of 

 the walls and p vanishes on the others. 



So far the amplitude factors A^ have been regarded as 

 arbitrary. However, since the vector displacement must 

 satisfy the basic relation 



P o ^ +v £ = (57) 



A t = BK t (58) 



where B is a single arbitrary constant. Accordingly the 



47 



