224 BELL SYSTEM TECHNICAL JOURNAL 



Thus it appears that the resistance modulation must always be greater 

 than the mass modulation and when the difference is small the air 

 momentum must be increased to compensate. Owing to the physical 

 limitation in accuracy of continuous maintenance of adjustment in 

 the larynx, if a large momentum is depended upon to compensate for 

 a small modulation difference, an unsteadiness or instability is likely 

 to result. It is common experience that it is impossible to produce a 

 sound with the voice with less than a certain minimum intensity. 

 This corresponds, with the most favorable adjustment of the modu- 

 lation constants which are physically possible, to a minimum momen- 

 tum of air from the lungs which satisfies (46). It will be evident 

 that this interpretation must not be taken too seriously quanti- 

 tatively. 



Subsidence and Accretion of Vibration of the Simple Larynx 



Oscillograms made of the speaking voice show that, among other 

 things, the amplitude of the oscillation and the pitch are in a con- 

 tinuous state of change. This is also true in singing but not nearly 

 to the same extent. It seems therefore that in singing the adjust- 

 ment of the voice system for sustained oscillation as described in 

 (44) above is of major importance, while in speaking conditions for 

 variation are of most importance. 



The principle of the investigation of variation is simple enough 

 but in all but the most elementary systems the algebra involved is 

 impracticably awkward. If by solving {ii) directly for the roots of p, 

 it be found that A is positive, then any existing vibration will tend to 

 increase while if A is negative, then vibration will tend to subside. 

 The algebraic difficulties arise in the general solution but these are 

 largely obviated by making the assumption, which is most likely 

 usually fulfilled in practice, that the real parts of the roots may be 

 treated as small quantities when compared with the imaginary parts. 

 A common frequency for a man's voice is 150 cycles per second for 

 which coo is 1000 in round numbers. The decrement of a telephone 

 receiver is ordinarily 100 to 200 in open air. The decrement of a 

 tuning fork is represented by a fraction. Judging from variations 

 in amplitude in an oscillogram (from which of course decrements 

 may not be read directly) it would seem reasonable to assume that A 

 is small compared with wo- The study of variation thus becomes an 

 investigation of small departures from a condition of sustained oscil- 

 lation, the reference condition being that critical adjustment for which 

 the roots of interest of {ii) are pure imaginary. 



