I9IS.] SURFACES OF TELEPHONIC DIAPHRAGMS. 109 



Application of Circular Velocity-Diagram Theory to 

 Results of Explorations. 



It is shown in the first-approximation theory of Appendix II., 

 that the behavior at the center of a flat-clamped circular diaphragm, 

 subject to constant vibro-motive force of varying frequency, can be 

 completely predicated, if three constants of the diaphragm are 

 known ;* namely, 



(i) the "equivalent mass" m (gm.), 



(2) the elastic constant s (dynes per cm. of displacement at 



center), 



(3) the mechanical resistance r (dynes per unit velocity at 



center). 

 All these three constants can be obtained, for an acoustically excited 

 diaphragm, with the aid of the vibration explorer. 



Determination of m. 



In order to determine the equivalent mass of a diaphragm, it 

 is necessary to know the distribution of amplitude over the entire 

 vibrating surface. As is shown in Appendix III., when the dis- 

 tribution of amplitude conforms regularly with the Rayleigh 

 formula, it would appear that the equivalent mass is 0.183 times the 

 mass of the circular vibrating plate. If, however, the distribution 

 of amphtude is irregular, such as may be produced by bipolar elec- 

 tromagnetic excitation of a telephone-receiver diaphragm, the coeffi- 

 cient 0.183 cannot be depended upon, and the proper coefficient must 

 be determined by some process of quadrature, such as Appendix 

 III. describes. 



The Elastic Constant .y. 



The constant .y is the inferred elastic resisting force, which, 

 acting perpendicularly upon the diaphragm's equivalent mass (at its 

 center), would produce the same effect upon the vibratory motion 

 as the distributed elastic forces produce upon the diaphragm's dis- 

 tributed mass, in the presence of the particular impressed force 

 distribution. The simplest way to find ^ is to measure the natural 

 fundamental frequency n^ of the diaphragm, by exciting it with an 



4 See Bibliography No. 8. 



