102 



THE STUDY OF SPEECH CURVES. 



Figure 67 is the same curve as that in figure 93 without friction. It is 

 evident that if we know the factor of friction s we can calculate the fric- 

 tional element e~" for each value of t ; then by multiplying each ordinate 

 of the curve in figure 95 by e " we shall obtain the ordinates of the curve 

 in figure 67. In other words, to turn the simple sinusoid into the fric- 



tional sinusoid we multiply each ordinate by e~" = — (or divide by e") ; to 



turn the frictional sinusoid into a simple one, we reverse the process and 

 divide by e~" (or multiply by e'')- 



Suppose now that we have a wave concerning which we know only 

 the period T and the factor of friction e, and that it was produced by 

 one or more frictional sinusoids, for example, the wave in figure 94. To 

 obtain its elements we must analyze it into a series of frictional sinusoids. 



By multiplying each of the ordinates of the curve by the appropriate 

 value of e" we turn the curve into the corresponding simple sinusoid with 

 the friction eUminated. The new curve is then the sum of a number of 

 simple sinusoids, and we can use the harmonic or the inharmonic analysis 

 to find its elements. 



This analysis presupposes that the factor of friction £ is known; in 

 the case of a curve resulting from a single element, as in figure 93, it 

 can be obtained by measuring the successive amplitudes and performing 

 a simple calculation in the manner indicated at the end of this chapter. 

 In more complicated curves it can often be approximated when one of 

 the components is much stronger than the others; an illusti alien will Le 

 given in Chapter XI. 



