EXAMPLES OF VOWEL ANALYSIS. 



141 



1/15.5 that of the fundamental, or 34.0 and 23.2mm. Taking the maximum 

 ordinate as the amplitude of the inharmonic we have as a result the three 

 sinusoids with the wave-lengths 100.0, 34.0, 23.2mm. and the amplitudes 

 44.3, 2.5, 1.7mm. These inharmonic components are given in figure 122. 



Fig. 124. — Curve of figure 121 with friction eliminated 



For an analysis into frictional sinusoids 

 (Chapter VII) the factor of friction (p. 106) 

 must be found. Using the maxima and minima 

 we perform the adjacent calculation. The first 

 cohimn contains the maxima and minima, the 

 second the differences between successive values. 

 The third gives the natural logarithms. From 

 the last column we have to calculate 



^_ g 5(5. 1240 - 4.4886) +3(4.9698 - 4.5326) + (4.9558 - 4.6250) _ q ^g-,^ 



6 X 35 



Since the period T of the vibration from which we calculate d is 



very closely 100 we have 



2d 

 £=y^= 0.0028. 



The calculation rests on the assumption that for this purpose we can 

 treat the given curve like a single frictional sinusoid. If it were such a 

 curve the differences between the successive maxima and minima would 

 have a constant relation. In the given curve the differences are 168, 144, 

 138, 102, 93, 89; the relation of each to the following one is 1.17, 1.05, 

 1.36, 1.10, 1.05 respectively. Instead of being constant the relation 

 varies considerably. It is due to the fact that the curve is compounded 

 of several simpler curves and the maxima and minima result from their 



