306 Free Path Phenomena [CH. xvi 



This corresponds physically to propagation with velocity V, the whole 

 wave motion being damped with a modulus of decay 



2 2 



35*VK7 (739) ' 



per unit length. 



Thus the first effect produced by the slowness of adjustment between 

 internal and translational velocities will not be a change in the velocity of 

 propagation, but a damping of the sound. 



364. There is a second cause which tends to diminish the amplitude of 

 a wave of sound propagated in free air, namely the viscosity of the gas. 

 This has of course been neglected in the present investigation because we 

 have assumed Maxwell's law to give a sufficiently good approximation an 

 assumption which, as is evident from the last chapter, includes the neglect 

 of viscosity. The effect of viscosity* is to introduce a linear modulus of 

 decay 



''' < 740 >- 



proportional to the first power of the coefficient of viscosity K, when K is 

 small, and to alter the velocity of propagation only by terms depending on 2 . 



It will be noticed that expressions (738) and (739) are both proportional 

 to p 2 , so that their ratio depends only on the gas, and not on the frequency of 

 the sound. The effect of the lag in rotatory energy can accordingly be fully 

 allowed for by supposing K increased to 



3raF 2 

 35/3 Vl< ' 



14K 

 Since, by equation (737), F 2 = , this expression can be written in the 



form 



The last term is independent of the density and proportional to the 

 square root of the temperature, as also is K. Hence formula (741) is the 

 mathematical expression of an increase in K which depends only on the 

 structure of the molecules and not on the state of the gas. To determine 

 the amount of this increase, we use the formulae 



K ^mvcl ( 301), 



(131), 



* See Lord Eayleigh's Theory of Sound, n. 346. 



