igis-] 



SURFACES OF TELEPHONIC DIAPHRAGMS. 



121 



tory motion were observed, in the range of acoustic impressed fre- 

 quency up to 1,700'—^. 



TABLE in. 

 Flat Circular Diaphragms. 



Appendix I. 



Application of Bessel-F unction Theory to a Diaphragm Vibrating 

 in its Fundamental Mode. 



Referring to Lord Rayleigh's "Theory of Sound," Vol. i, page 

 352, the formula for the instantaneous amplitude of free vibration 

 in a flat plate is, 



zVn=^P{Jn{kr) -\-XJn{ikr))cos{ne-^an)-cos{wt ^ e) cm.,.(i) 

 where subscript n = the number of nodal diameters (numeric), 

 zt'n = instantaneous amplitude at a point on the diaphragm whose 

 polar coordinates are r cm., 6 radians (cm.) 

 F= constant of amplitude-magnitude (cm.), 

 k = dL constant of the material defined by: 

 k^y^/c (cm.-^), 



c = a constant of the material defined by: 



qb'' 



I2p(l 



(cm. /sec.*), 



g = Young's modulus for the diaphragm material (dyne/cm.^), 

 p = density of the diaphragm material (gms./cm.^), 

 o-=Poisson's ratio for the diaphragm material (numeric), 

 & = thickness of the diaphragm (cm.), 

 A=:a constant satisfying boundary conditions (numeric), 

 /» = a Bessel's Function of the nih. order (numeric), 



* Thickness of japan 0.0074 cm. 



PROC. AMER. PHIL. SOC, LIV. 217 I, PRINTED JULY 6, I915. 



