EXAMPLES OF VOWEL ANALYSIS. 



153 



Although the three vibrations used for this calculation have not 

 exactly the same length, we can for the present purpose use one-third 

 of their combined length, namely, one- third of 28.4 for the calculation 

 of £. We have then 



_ 2d _ 0.45584 

 ' T 9.5 



0.0480. 



The calculation being made on the assumption that for this purpose 

 the wave can be considered as a single frictional sinusoid (p. 141), the 

 quotients of the successive differences between the maxima and minima 

 must be approximately constant. The differences for the wave in figure 

 130 are 8.3, 7.1, 6.3, 4.6, 4.1, and the quotients are 1.17, 1.13, 1.37, 1.12 

 respectively. The variation is great, but in the present case we have the 

 means of getting a more general average for the factor of friction. The 

 successive maxima and minima for the four wave-groups of the original 

 curve of figure 129 are 8.3, 1.1,6.0, 2.3,6.3,9.0, 1.2,6.8, 2.3, 6.1, 8.3, 2.0, 6.5, 

 1.7, 6.3, 8.3, 0.8, 7.1, 2.5, 6.6. The ratios of successive differences varj- 

 around 1.20 irregularly; we therefore assume that the variations in a single 

 set can be eliminated by taking the averages. The averages for the four 

 sets of differences are 8.5, 7.2, 5.3, 4.4, 4.1, and the ratios are 1.18, 1.36, 

 1.20, 1.07. Calculating the factor of friction in the way just illustrated 

 we obtain £ = 0.0492, a result so close to that for the original single wave 

 that we retain the original calculation for the further computation. 



Since each of the ordinates is to be multiplied by the corresponding 

 value of e" (p. 142), we have to perform the calculation which is indicated 

 in the adjacent table. We first obtain £.log e = 0.0480x0.4343 = 0.0208. 



