A. S. Iberall 

 Core Solutions 



Modes I and II (available at a glance from the core equations as independent 

 solutions X 7^ 0, and X = 0). e' ^ *"; bj = V-jM^ - \ (a repeated root): 



U = ja^b^flje'^i'' - jMQ[(l-a)\+ j(7-cr)q\/32MQ+ j (7 - <^) S/32g] S^ e ' ^i" , 



V = -jabj2(3je'^i'' + jaM^bJCl-a) + j (y - a) q/^^Mj S^ e'^'i'' , 



X = jSbj2(!je^^»'' , 



J = a(7- 1) SgbjSje^^i" , ^ - ■■■ ■■ • • •-- '- 



P = j(7-o-) qS/32M^gbj!Bje'*'i'' . "~ '" '■ "' '" ''■■"' 



These modes represent viscous diffusion. '- ' • 



Mode III (The mode is in the vicinity of D^ = -jctMq- \ from the J equation. 

 It is the thermal diffusive mode. If /3^ = 0, the solutions would be "exact." 

 The solutions presented are valid to first order in /3^.) 



±jb,x . 



e 3 . b3 = y-jaMg - \ + /32[(7- l)(l-cr-aq)M(,2 -j(y- 1) Sg] : 



X = , (■ • ,^- 



jb-x 



J = ae 



CTC. e 



'3' 



1 



jb,x 



■j (l-cr-aq)/32Mpeje^ 



'3' 



Mode IV (This is the elastic mode of propagation of pressure.) 



e''^^'' ; d^ = y\ - /32M„2 + js/32g + j [(^_ ly^^ l + q]/34M^3 . 

 U = -jdJaM„-j (\-d^2y3)^gd4- _ 

 V = a[aM„- J (\-d^2]3)^ed4'' ^ 

 X = 

 g- = .^Cy- 1) [M^2_ j(i+ q)(^_ d^2)M^- jSglSD^e'^^'' ^ 



P = J[^M,- j(\-d^2)]^jM(,+ (l + q)(\-d^2)]2)^e'^4" . 



716 



