ENERGY DISTRIBUTION IN SPEECH 121 



A second correction was made for the varying area of tuned circuit 

 curves. 



In Fig. 3 let S{j) be the speech spectrum determined by 'deal 

 methods; "i?" the transmission curve of the tuned circuit, set for a 

 resonant frequency/. An ideal transmission curve would be a rectangle 

 when plotted in this figure, of height "/^" and transmission range A/. 



The true amount of energy 5(0 associated with frequency/, and the 

 experimentally determined value which we may call (5/) are con- 

 nected by the relation 



hS{f)Af= r^'^^S{f)R{f)df 

 and if we make ^f 



w=y R{f)df 



we may take for all practical purposes S{J) = Sif), considering the 

 narrowness of the transmission range. We must therefore find the 

 factor h^f, proportional to the area of each tuned circuit curve and 

 divide the energy received through the filtered side by /?A/, in order to 

 obtain S{f). This treatment may be gone through for each syllable 

 individually, but it is more convenient to sum the tuned circuit read- 

 ings for all the syllables used, corrected one at a time for varying 

 volume, and then apply the curve area correction to this sum. 



A third correction was made for the varying frequency-sensitivity of 

 the whole apparatus. Thus far we have discussed only the electrical 

 energy in the output circuit of the fourth stage. It remains to show in 

 what way this is related to the mechanical energy of the diaphragm, 

 and this in turn to the incident sound energy. 



The calibration of the circuit as a whole was made by introducing a 

 small resistance carrying alternating current in series with the con- 

 denser transmitter, thus introducing a known potential drop in the 

 undisturbed input mesh of the circuit. 



An amplification curve is appended {A, Fig. 4) which gives to an 

 arbitrary scale the ratio of volts output to volts input as a function of 

 frequency, for the system as actually operated. The calibration of the 

 condenser transmitter, shown in Fig. 4, Curve C, gives the open 

 circuit voltage of the transmitter per unit pressure on the diaphragm 

 as a function of frequency. The product of these curves is the volts 

 output per unit alternating pressure on the diaphragm, and the square 

 of this product, curve E is proportional to the electrical energy output 

 per unit sound energy incident on the diaphragm, if we assume that 

 the sound energy is proportional to the square of the alternating 

 pressure. This point, however, requires some further discussion, 

 which will be given later on. 



