226 BELL SYSTEM TECHNICAL JOURNAL 



is the exponent, of the increment dKu and the frequency (imaginary 

 part) of vibration increases sHghtly in proportion. If K,, were the 

 only varying element the vibration would continue indefinitely to 

 increase. 



If on the other hand K„ be assumed constant, the variation being 

 in Ri, then it may be similarly shown that 



dp =1— T, 



- ( 4A, + -^ + Ao-^ ) + /""-^'^ 



Li\Li2 I COq 



(52) 



whence it appears that a small increase in glottis resistance dR\ (or 

 (/Ai) introduces a subsidence of vibration but an increase in frequency 

 of oscillation as before. A decrease — dR^ of course produces the 

 opposite efifect. 



If the change be in G, it turns out that 



dG 

 dp = 



ZcOo'LiyLiO 



A^-2GAo ) + /•( ^^^ + 2couG 



Wo 



(53) 



Here it appears that an increase in the gyrostatic mutual, G, may 

 introduce either a subsidence or an accretion in amplitude but like 

 the others makes for an increase in frequency of oscillation. 



Variation in other elements produces similar conflicting tendencies 

 not only in damping but in frequency. 



The physical picture to be drawn from this is that in speaking the 

 voice modulates from one amplitude and frequency to another by 

 proper relative variations in adjustments in its constants, being con- 

 stantly in a state of changing subsidence or accretion. It would 

 seem also that the principal cause of change in frequency is in the 

 vocal cords and that of amplitude variation in the glottis. Speaking 

 is, in this respect, a more intricate process than singing. 



Other Types of " Feed Back" 



The detailed study of the larynx has so far been limited to the 

 assumption that the " feed back" is entirely gyrostatic. This is of 

 course actually not the case. How much influence is exerted by the 

 general Yq is difficult to estimate. 



If the trachea were a long tube but still shorter than a quarter 

 wave-length of sound at the frequency of oscillation and rather smaller 

 in diameter, and substantially open at the end the mass of the air 

 in it would then be appreciable and Fo in (30) would be written p''Lo. 

 If in addition the gyrostatic term were negligible the system would 

 then be exactly analogous with the tuned grid system and (32) rather 

 than (31) should be the subject of detailed study. 



