Thus the attenuation factor (3 associated with viscosity is 

 supplemented by an additional term related to the thermal 

 conductivity of the medium. For water the magnitude of 

 the attenuation associated with conductivity is about 1/10 

 of that due to viscosity under normal conditions. In view 

 of this, the neglect of conductivity seems to be justifiable. 

 However, for greater accuracy, the effect of conduction 

 can be included within the framework of the viscous theory 

 alone by employing the quantity 



Kb 3 T n \ r 

 (2^ +\ x ) + 



°P 



as an effective viscosity in place of (2 p. +X ). 



SOME SPECIAL SOLUTIONS OF THE WAVE 

 EQUATION 



Plane -Attenuated Sound Wave 



The particle displacement for a simple harmonic, 

 plane sound wave, in a fluid with viscous losses and prog- 

 ressing in the x-direction, can be written 



s = s e j(wt-kx) e -a^x (34) 







where j = /-l, h is the wave number, «j the frequency and 

 s is the amplitude of excursion of the fluid particles. The 

 last term containing a^ is the attenuation term. This can 

 be included in the propagation constant by allowing k to 

 assume complex values. The complex wave number /t* is 

 accordingly 



ft* = h - j a h (34) 



41 



