Hence, (33) takes the form 



s = So ej(t»t-^*x) (35) 



For simple harmonic waves it follows that 



|7=jws (36) 



at 



and therefore the scalar counterpart of (15) takes the form 



|!# = ^ (1+>B) |!£ ,37) 



where 8 is the viscous time factor defined by (21). It is 

 convenient to introduce a complex sound speed 



o*=(— ) (1+JwVf. (38) 



and thereby recover the canonical form 



c* 2 ^-f- (39) 



The relation (35) is consistent with (39) provided that 



o* k* = uu (40) 



where uu is regarded as real. Thus the complex wave number 

 is given by 



h - ja k = w(^J (l+juu0) (41) 



K \ p 



42 



