Physical Measurements of Audition and Their 

 Bearing on the Theory of Hearing * 



By HARVEY FLETCHER 



Synopsis: The author states his purpose to be the presentation of cer- 

 tain facts of audition which have been determined recently with consider- 

 able accuracy and the discussion of the theory which best explains these 

 facts. 



Making use of data of Knudsen's as well as his own measurements of the 

 auditory sensation area, the author estimates that the normal ear can 

 perceive approximately 300,000 different pure tones. This is taking ac- 

 count of all possible variations in both pitch and intensity. Knudsen's 

 data show that for considerable ranges the minimum perceptible difference 

 in intensity bears a constant ratio to the intensity and the minimum per- 

 ceptible difference in frequency bears a constant ratio to the frequency. 

 These relations have been termed by psychologists "The Law of Weber 

 and Fechner." 



A loudness scale is proposed such that the difference in loudness between 

 two tones is equal to ten times the common logarithm of their intensity 

 ratio. A pitch scale is proposed such that the difference in pitch is equal 

 to one hundred times the logarithm to the base two of the frequency ratio. 

 A method for measuring the loudness of complex sounds is mentioned but 

 is to be discussed in a later paper. A method is proposed for expressing 

 quantitatively different degrees of deafness. 



Reference is made to data obtained by the author on the masking of one 

 pure tone by another. The minimum audible intensity of a pure tone 

 depends upon the presence of another tone of different frequency. A low 

 pitched note will, in general, exert a surprisingly large masking effect 

 upon notes of higher frequency. The masking of a low note by a higher 

 is not nearly as pronounced. From his observations, the author draws 

 certain interesting conclusions. For example, given a complex tone con- 

 sisting of three frequencies 400, 300 and 200 cycles with relative loudness 

 values of 50, 10 and 10, respectively, the ear would hear only the 400 cycle 

 tone and the 200 cycle tone. If the sound is now increased 30 loudness 

 units, without distortion, the 400 cycle tone and the 300 cycle tone only, 

 will be heard. 



Binaural masking in which each ear receives one of the two sounds is 

 considered and the conclusion reached that the masking effect noted 

 results from conduction of the masking tone through the bones of the 

 head to the ear receiving the masked tone. 



It is stated on the basis of data obtained by Wegel and Lane that the 

 oscillatory system of the ear, comprised by the membranes and little 

 bones of the middle and inner ears, does not obey Hooke's Law regarding 

 the proportionality of stress and strain. Consequently, the ear, when 

 stimulated by a pure tone, introduces harmonics and the workers cited 

 have observed harmonics as high as the 4th order. The non-linear trans- 

 mission characteristic of the vibratory system of the ear is held to account 

 for the greater masking of a high frequency by a lower. 



A theory of hearing is advanced which pictures the basilar membrane 

 as being caused to vibrate by incident sound waves. In the case of a pure 

 tone, the membrane is supposed not to vibrate uniformly throughout 

 its length but the region of maximum amplitude determines the pitch of 

 the tone as interpreted by the ear and the maximum amplitude deter- 

 mines the intensity. — Editor. 



THE question of how we hear has been a subject for discussion 

 by scientists and philosophers for a long time. Practically every 

 year during the past fifty years articles have appeared discussing the 



* Presented at the meeting of the Section of Physics and Chemistry of The Franklin 

 Institute held Thursday, March 29, 1923, and published in the Journal of the Franklin 

 Institute for September, 1923. 



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