LOUDNESS 



407 



represent the results. When the values of b^ derived In this way were 

 plotted with bk as ordinates and A/ as abscissae and Lk as a variable 

 parameter then the resulting graphs were a series of straight lines 

 going through the common point (- 250, 0) but having slopes de- 

 pending upon Lk. Consequently the following formula 



bk = [(250 + A/)/1000](2(L,) 



(17) 



will represent the results. The quantity Af is the common ditYerence 

 in frequency between the components, Lk the loudness level of each 

 component, and Q a function depending upon Lk- The results indi- 

 cated that Q could be represented by the curve in Fig. 11. 



20 



40 60 80 100 



UOUDNEISS LEVEL OF COMPONENT-DB 



120 



Fig. 11 — Loudness factor Q. 



Also the condition must be imposed upon this equation that b is 

 always taken as unity whenever the calculation gives values greater 

 than unity. The solid curves shown in Fig. 10 are actually calculated 

 curves using these equations, so the comparison of these curves with 

 the observed points gives an indication of how well this equation fits 

 the data. For this series of tones Q could be made to depend upon 

 /3a- rather than Lk and approximately the same results would be ob- 

 tained since ^/,. and Lk are nearly equal in this range of frequencies. 

 However, for tones having low intensities and low frequencies, ^k will 

 be much larger than L/, and consequently Q will be smaller and hence 

 the calculated loudness smaller. The results in Figs. 8 and 9 are just 



