Wu 



Oscillotory - 2 mode 



2.0 k,//3 (or k,//9) 



1.0 



2.0 



Fig. 2 - Projections on the kj.-k^ plane of 

 lines in Fig. 1 



The group velocity c of these waves is 



Boj 



3a) 'bco 



'E 3k \3k^ ' Bk„ ' Bk. 



X y i 



(48) 



which is the gradient of ^ in the k space; hence c^ is everywhere orthogonal to 

 w = const, surfaces, which are hyperbolic surfaces of revolution (about k^-axis), 

 in the direction of w increasing. From (45a) and (48), 



Cg = A cos cp (k^ cos 2^ + /32)/(k2 + ^2) , 



A sin cp (k^ cos^^ + ,62)/(k2 + ^2^ , 

 - Ak^ sin e cos d/{\i'^ \ fi'^) . 



(49) 



560 



