DYNAMICAL STUDY OF THE J'OWEL SOUNDS 113 



nasal cavities are brought into play. The calculations required would 

 be too cumbersome for the present paper. It is rather a tribute to 

 Paget's experimental skill that he was able to synthesize these more 

 complicated sounds with resonators of more than two degrees of free- 

 dom and so arrive at their characteristics. 



It is not thought that the calculations given herein suffer appreciably 

 due to the omission of damping factors from the dynamical equations. 

 It would be almost impossible to take correct values of damping 

 constants from the speech spectra ; there is a better chance of doing this 

 from the records of the sounds themselves, but even so, they cannot be 

 determined with anything like the precision of the natural frequencies. 



To summarize the results, we have an idealized system of two de- 

 grees of freedom, loosely coupled for one gioup of the sounds, closely 

 coupled for the remaining sounds, with fair indication of the transition 

 between the two groups. We have the assumption of virtually con- 

 stant total volume of the two cavities, and an indication of how this 

 volume should be apportioned between them in most cases. We also 

 have a rough determination in most cases of the conductivity o<" the 

 inner orifice between the two cavities. 



Some Experimental Tests 



It would be of interest if we could now make models of all the 

 systems considered, excite them in some suitable way, and establish 

 their essential validity from the character of the sounds produced. 

 This might seem unnecessary, on account of Sir Richard Paget's ex- 

 tended work; it seemed worth while, however, to attempt a few models, 

 using cardboard tubes and plasticene for the structure. 



The most success was had with the sound a (father). A model 

 was made to scale (Fig. 6), using the data of the chart — but of course 



Jo 



Air Supply 



Fig. 6 — Double resonator model for a, and method of attaching artificial larynx 



we should expect similar results from somewhat larger or smaller 

 models, provided the ratios Ki : K-i : V\ : F2 were maintained ; 

 the chief point here is the variation in damping with the sizes of the 

 orifices, and the requirement that any orifice should be smaller than 

 8 



