THEORY OF VIBRATION OF THE LARYNX 111 



If on the other hand the lungs acted substantially as a solid walled 

 chamber of comparatively small size, the elasticity of the contained 

 air would be represented by taking K^ for Fo. The surface area in 

 the lungs is very large compared with a regular chamber of equal 

 volume so considerable dissipation must be encountered by vibration. 

 If this were the most important reaction Fo should have been replaced 

 by pR^. 



Unquestionably all three types of reaction enter. A more general 

 treatment to include them is plainly not a subject for a short paper. 

 It is interesting however to note that in the dynamical system of 

 brass horns these latter Fo reactions exert controlling influences. In 

 this case the lips of the player perform the same function as do the 

 vocal cords of the voice while the external load, the horn, corresponds 

 to the pharynx, the reaction of which is the same dynamically as 

 the trachea. In this case the frequency of the horn is that of sustained 

 oscillation and not that of the lips. The same is true of the wood- 

 wind, in which case the reed or reeds replace the lips or vocal cords. 

 In these cases Fo is proportional inversely to the hyperbolic tangent 

 of the frequency or may be approximately represented by the im- 

 pedance of an anti-resonant element. 



