FL UCT UA TIONS IN MICROPHONES AND THER RESISTA NCES 2 1 7 



Considering the difficulty in holding a fixed granular configuration in 

 a cell of loose contacts we feel that the experimental results justify the 

 conclusion that the assumptions underlying the derivation of Eqs. (6) 

 and (7) are essentially correct, which require that the phase of the noise 

 voltage from each unit cell is entirely independent of that of any other 

 cell in the aggregate. From this we conclude that the mechanism 

 causing the noise is a small-scale effect capable of independently 

 existing within a volume element much smaller than the size of the unit 

 cell in any of the experiments we have performed on aggregates. In 

 fact, as will be assumed later, we believe the noise mechanism to be 

 located in a volume element smaller than that concerned with the 

 properties of a contact between two particles. 



If resistance elements are so chosen that each has the same resistance 

 and noise, and these are placed in a circuit where the impedance Z is 

 large compared to the resistance of the elements, then Eqs. (6) and (7) 

 can be written respectively as follows: 



n 

 and 



FAeries = ne\ (7a) 



The resistance Roi a parallel assemblage of like contact elements, each 

 having the same resistance Rk, is obtained from 1/R = n/Rk, or 

 n = Rk/R. 



Substituting this in Eq. (6a) we get 



K-k 



For like contact elements in series we get n = R/Rk, hence Eq. (7a) 

 becomes _ 



F2 . = — 



' c series d 



Kk 



(7b) 



If now we have the further condition that the battery voltage is so 

 adjusted for each new assemblage that e- is always constant, then Eqs. 

 (6b) and (7b) are equivalent and we have 



V7 = Const. R. (8) 



An equivalent relationship was derived and experimentally tested by 

 Otto,^ but it is clear from our derivation and measurements that it 

 applies only to a change in the assemblage of like contacts, such as is 



