Chap. 9] SEISMIC METHODS 481 



sidering both spreading and absorption, 



.— ar 



for a spherical wave. The absorption coefficient a appears to increase 

 with the second power of the frequency. Hence, high frequencies are 

 largely eliminated with increasing distance from source of vibration and 

 the low frequencies are left over. According to Stewart and Lindsay^" 

 the following relation exists between absorption coefficient and viscosity: 



where 11 is the Poiseuille coefficient of interior friction. 



Damping constants may be determined in the field and laboratory from 

 resonance curves. The latter are taken with the apparatus previously 

 described (see pages 462-463), the former with vibrators. In both cases 

 the medium under test is force driven, and its dynamic magnification W 

 (see page 602) is given by 



V = :^~^~^., (9-39a) 



where n is the tuning factor or the ratio of impressed and natural frequency 

 w/ojo , and rj is the relative damping (see page 586) in per cents critical. 

 Substituting in the above formula the resonance tuning factor n,. = 

 a/I — 27/2, the magnification at resonance 



For the determination of r] from a resonance curve it is convenient to 

 measure the frequencies at which, below and above the resonance peak, 

 the maximum amplitude has dropped to l/\/2 of its peak value. Then 

 a combination of the last two equations gives 



4v' l-n' 



VWmax./ (1 - 



n^y _|_ 4,j2^2 



or I? = 



and with W = Wmai./\/2: 



1 ,v,2 /2 /.2 



I — n Jo —J 



■n = 



2V2-n2 2/0V2/S-/ 

 " Loc. cit. 



(9-39c) 



