Useful Numerical Constants of 

 Speech and Hearing 



By HARVEY FLETCHER 



Ndtk: The material given in this p;iper was prrparoil in ,i more con- 

 ilensol form for piililiratlon in the International t ritical Tables. In order 

 to make it available in convenient form for the use of telephone engineers 

 it was ileemeil atlvisable to publish it in this journal. The author is 

 intlebtc<l to Dr. J. C. Steinlierg for able assistance in collecting and 

 arranging the material. 



I Ullll lOf.RAlMIV 



Al}lHI.I()t'il\.\l'll 1)1 (Kipcrs on I'iirli Discrimination, Intensity 

 niscrimination, Absolute Sensitivit\' of the Ear, I'pper Limit 

 of Autlibility, Lower Limit of Au<lii)ility, Theories of Hearing and 

 other miscellaneous works on Speech and Hearing are given in a 

 pafH>r by H. Fletcher, Bell Tech. Jour., Xol. H, 4, pp. 178-180, Oct., 

 1023. 



11. .AnsoiA'TE Sexsitimtv of the Ev\r 



The sensitivity is the minimum audible rins pressure in dynes 

 cm~- in ear canal. The values below are the average of the results of 

 Wien (Arch. f. ges. Physiol. 97, p. 1, 1903), Fletcher and Wegcl 

 (Phys. Rei:. 19, p. 'yn.i. June, 1922), and Kranz (P/»V5. Rei<., 21. p. .57:?, 

 May, 1923) weighted 3, 72. and 1 L respectively according to number 

 of ears tested 



T.ABI.t: I 



Frequencv (dv)' 64 12S 256 512 1024 204,S 4t)% 



Sensitivity (dynes I 12 .021 .OO.V) .(X)l 00052 (K)04I 00042 



111. MiNtMiM Audible Power for a Normal Ear 



The power in microwatts passing through each square centimeter 

 in the wave front of a free progressive wave in air under average 

 conditions is related to the rms pressure in dynes by the formula 



P = 20.WJ- 



The figures of Table I may be converted by this formula to minimum 

 audible powers. It is thus seen that the minimuin audible accoustical 

 power is at freciuencies between 2,000 and 4,000 vibrations per second 

 and is equal to 4X10"'° microwatts per square centimeter 

 ' The symbol dv is used to denote "double" or complete vibrations. 

 375 



