482 



SEISMIC METHODS 



[Chap. 9 



Since, in approximation, / = /o in the denominator, the damping rates 

 become, for two frequencies, /i and f% , at which the djoiamic magnifica- 

 tion has fallen off to one-half of its maximum value: 



■ni = 



2fl 



and 



m 



^ -iSl-fl) 

 2fi 



so that, since 



/l+/2_ , 



—2 •^°' 



V = 



^1 + Vi _ h ~/i 

 5 2/o 



(^39d) 



Since the damping resistance p, or the ratio between driving force and 

 velocity of motion (see page 584), is given by p = 2mt, with m as mass 

 and e equal to woij, the damping coefficient e is irA/; therefore the damping 

 resistance (or dissipative resistance) 



p = 2irmA/. 



(9-40) 



(For tofsional vibrations the polar moment of inertia is substituted for 

 the mass m). Table 57 gives the damping resistances of a number of 

 substances in bar form at 10 kc (p in kilohms), as found by Wegel and 

 Walther.'' 



Table 57 

 DAMPING RESISTANCES OF SUBSTANCES IN BAR FORM 



Lead 117-130 



Hard rubber 25.5 



Nickel 10 



Copper 5.5 



Silver 2.8 



Glass 2.45 



Steel 0.84 



Steel (annealed) 0.215 



Similar determinations for rocks have not been published, but they 

 would undoubtedly add greatly to our knowledge of dissipation and ab- 

 sorption of seismic energy. From the damping, an equivalent Poisseuille 

 coefficient IT may be derived if the vibrating medium has a simple geometric 

 shape, such as a bar oscillating longitudinally. In such a case the viscosity 

 coefficient is 11 = pZ/27r^S, S being the area of the rod. Substituting 

 m = US for its mass, n = pZ^5/27r^m. Since, from eqs. (9-29a) and 

 (9-296), 



/^5 = 



it is seen that 



E 



n = 



p£ 



8x^771/0' 



and, since 77 = 



4Tm/' 



Hw 

 £ 



(9-41) 



The relative damping is thus represented by the ratio between a dissipa- 

 tive modulus Hw and the elastic modulus. Hence, in a complex representa- 



« Physics, 6, 141-157 (April, 1935). 



