58 BELL SYSTEM TECHNICAL JOURNAL 



quantitative measurements of each of them on a rigorous statistical 

 basis. 



The statistical deviation from the mean varies irregularly with fre- 

 quency; very likely this is due mostly to the external anatomical 

 variations in ears which cause deviations in the dynamical constants 

 of the transmission system from sound source to the ear drum. The 

 dotted lines following the curve of minimum audibility represent 

 approximately the "standard deviation." 



3. Maximum Andibility. The curve marked "Maximum audi- 

 bility" represents the logarithmic average pressure on 48 normal ears 

 required to produce the sensation of feeling. This represents the 

 threshold of feeling in the same way that the minimum audibility 

 curve represents the threshold of audition. A sound much louder 

 than this is painful. The measurements were taken through a range 

 of from 60 to 3,000 cycles. The standard deviation lines are also 

 given from which it will be seen that this curve is quite as definite as 

 that of minimum audibility. While this point of feeling probably has 

 no relation to the auditory sense it does serve as a practical limit to 

 the range of auditory sensation. A few observations indicate that 

 people with abnormal ears have a point of feeling sound which is not 

 greatly different from that of normal ears, but this, of course, depends 

 on the type of abnormality. The intensity for feeling is about equal 

 to that required to excite the tactile nerves in the finger tips. 



4. Loiver and Upper Frequency Limits of Hearing. The curves of 

 minimum and maximum audibility in Fig. 1 will be seen to have been 

 extrapolated to the points of intersection at high and low frequencies. 

 The feeling sensation in the middle range of frequency is first a tickling 

 sensation and then becomes acutely painful as the loudness is in- 

 creased. As the frequency is decreased the sensation of feeling becomes 

 milder until frequencies around 60 cycles it is sensible as a flutter, 

 but still quite different from the sense of audition. As the frequency 

 is still further decreased to a point where the hearing and feeling lines 

 appear to intersect, it is difficult to distinguish between the sense of 

 hearing and that of feeling. The low point of intersection of the two 

 normal curves of minimum audibility and feeling sense may, there- 

 fore, be taken arbitrarily as the lower tone limit of audibility. For 

 frequencies lower than this it is easier to feel than to hear the air 

 vibration. The point of intersection cannot be determined by direct 

 observation due to the diflficulty in distinguishing between the two 

 sensations. A .similar intersection of the two curves occurs at some 

 very high frequency. Sound waves of frequencies below the lower 

 intersection and above the upper intersection are more easily sensed 



