.■insTR.icrs oi- bi-li. svsriiM Tnci/xiciL I'Ait.rs 215 



energy lre(iuenc\- spi'ctriini and i(s Ic\ el al)o\e the threshold ot hear- 

 ing and ihal il this rclat ionshij) hr represented as 



10 

 /> = -- log,,, 





sounds whose calculated values L are equal w ill appear equally loud 

 to the a\'erage normal ear. Pi is the r.m.s. pressure of the /th com- 

 ponent of the sound \va\-e. The weight and root factors 11' and r, 

 respectively, are functions of the sensation lexcl, which is synonymous 

 with the term loudness as formerlv used and is defined as 



■S=10 1cgi 





p,r- 



where Poi is the r.m.s. pressure of the /th component when the com- 

 plex sound is at the threshold of hearing. In case the components in 

 a narrow band of frequencies An are not resoh^ed their energy must 

 be integrated to obtain the energy of the equivalent single component. 

 The root factor r is inversely proportional to the ratio of the minimum 

 perceptible increase in energy to the total energy. For intensities 

 near the threshold, the weight factors are equal to the reciprocals of 

 the minimum audible pressures. Curves are given showing the 

 values for H' for various frequencies at various sensation levels, also 

 the values of ?- as a function of S. As the intensity is increased the 

 weight factors give greater weight to the lower frequencies; hence, 

 even though the amplitude of the sound wave be increased without 

 distortion, the ear will perceive both an increase and a distortion. 

 This effect is due to the non-linearity of the ear. 



Binaural Beats. C. E. Lane.^ By introducing a tone of frequency 

 / into one ear and another tone of frequency /+iV into the opposite 

 ear, where N is less than 5 or 6 cycles, two kinds of binaural beats 

 are obtained. Objective binaural beats are heard for most values 

 of / within the audible frequency range, provided there is the proper 

 difference in amplitude betw^een the two tones. For telephone re- 

 ceivers as sound sources, this difference for best beats is about 55 TU 

 and for the same receivers supplied with sponge-rubber cushions 

 about 62 TU. These beats are heard because the louder tone is con- 

 ducted through the head to the ear of the weaker tone and the two 

 tones there are about equally loud. Subjective binaural beats are 

 heard for frequencies below 800 or 1 ,000 cycles when the tones at the 



3 Physical Review, Vol. 26, No. 3, Sept., 1925. 



