VIBRATING TELEPHONE DIAPHRAGMS. 449 



called the bhtntness of resonance, in this case 9.006 X lO'^. The 

 semicircular range of resonance may be expressed in angular velocity 

 measure, as the range of angular velocity o).^ — oj^ between quadrantal 

 points, or 2A, in this case 56.6 radians per second. The same range 

 may be expressed also in frequency measure by n.^ — n^, or the dif- 

 ference of frequencies at quadrantal points =A/7r, in this case g — ■. 

 All frequencies outside of these quadrantal points may be regarded 

 as outside the semi-circular range of tuning. At the frequencies 

 of these quadrantal points, n.-,, n^, the resonant kinetic energy mani- 

 festly falls to one half. 



Referring to the dotted curve ABODE, Fig. 15, of the undis- 

 torted amplitude of the diaphragm's vibration, the ordinates Bb and 

 Dd indicate the amplitudes bounding the resonant range. The ex- 

 pressions defining these ordinates .x\ and Xr, are : 



— = — p • — and — = — p • — , numeric, (iQa) 



.To V2 Wl Xq -yJ2 71 2 



These ordinates are 6.35 and 6.0 microns, respectively, in Fig. 15. 

 The resonant range is 778 — 732 = 46 ---', and the resonant sharpness 

 is thus 753.5/46=16.4. It is thus possible to determine the sharp- 

 ness and the range of resonance from a curve of amplitude against 

 frequency, as well as from a circle diagram of velocity or of im- 

 pedance. 



The sharpness of resonance may also be defined by the acoustic 

 interval or numerical ratio e between the quadrantal frequencies. 



This criterion c is connected with the resonant sharpness A by the 

 relation 



A = , numeric, (22) 



c — I 



since any pair of frequencies, lying on the velocity circle, at equal 



