the conductivity and T the anomaly of temperature from 

 the mean value T . The linear approximation* for the 

 change in r\ is accordingly given by 



Br, 

 3£ 



K 



Po^n 



v 3 T 



(30) 



Now since the process is considered nearly isentropic, 

 it is reasonable to suppose that (2 7) can be employed as an 

 approximation for T in terms of p, with T and p taken as 

 their mean values and T and p identified with dT and dP 

 respectively. This approximation renders (30) in the form 



9r 1 __ 

 H p, 



Kb 



v 2 p 



(31) 



Accordingly (2 9) can be approximated by 



3£ 



bt 



P 



o p 



v 2 p - X c 



b® 



(32! 



where k is the thermal diffusivity (K/p Q O v ). Relation (32) 

 implies that the plot of p versus ® depends upon the char- 

 acteristics of the acoustic waves (e. g. , the frequency) as 

 well as the properties of the medium. Moreover, p and 

 are. not exactly in phase as implied by (7). 



If (32) is employed in place of (7) then the wave equa- 

 tion (in terms of p) takes the form 



rp 

 zt 3 



Kb*T n 



+ 8 +■ 



Or 



9t 



(33) 



*There will exist a steady increase of r\ with time associ- 

 ated with the attenuation; however, this is of second order. 



40 



