NATURE OF LANGUAGE — JONES 495 



Figure 4 is a plot of auditory sensation for the average human 

 ear. The lower curve shows the sensitiveness of the ear for sounds 

 of different pitches and is called the threshold of hearing. The data 

 were taken by measuring the least sound which could just be heard at 

 each of a number of frequencies. The sensitivity is measured in 

 terms of the minimum audible sound pressure while the frequencies 

 are arranged according to musical intervals (logarithmic scale). The 

 upper curve shows the extreme values of loudness at which the ear 

 begins to experience the sensations of feeling the vibrations. This 

 is the threshold of feeling and may be considered practically as a 

 maximum audibility curve. Sounds much louder than these are 

 painful. The two curves enclose the area of audition. The data 

 have been extrapolated at high and low frequencies to the points of 

 intersection, the extrapolation being guided to a certain extent by 

 other available information. At frequencies in the neighborhood 

 of sixty cycles a high intensity is felt as a sort of flutter. As the 

 frequency is lowered still further to the point where the hearing 

 and feeling lines appear to intersect, it is difficult to distinguish be- 

 tween the two sensations. For frequencies lower than this it is easier 

 to feel than to hear the air vibration. A similar intersection of the 

 two curves occurs at a very high frequency. This appears to give 

 a logical basis for defining the frequency limits of hearing, and as 

 seen from the plot they are about 20 and 20,000 cycles respectively 

 for persons of average hearing. At the lower and upper limits of 

 audition it takes about a hundred million times as much energy to en- 

 able one to hear as it does in the range of 1,000 to 5,000 cycles where 

 the ear is most sensitive. At all frequencies the energy required is 

 small, and in the most favorable region the minimum audible tone 

 corresponds to a pressure change per square centimeter of about 0.001 

 of a dyne. This pressure is roughly equivalent to the weight of a 

 section of a human hair about one-thousandth of an inch long (about 

 one-third as long as its diameter). 



In the portion of the audible region mcst commonly used, it is 

 found that the smallest change in the intensity of a tone which is 

 just discernible, is equal to about one-tenth of its original value. In 

 other words, in general the law connecting loudness discrimination 

 with the energy of the tone is a simple logarithmic one. It has been 

 proposed that change in loudness sensation be measured in units such 

 that a loudness change is equal to ten times the common logarithm 

 of the ratio of the energies. 



It has, been found that the law of pitch sensibility is approximately 

 logarithmic also. The fractional change in frequency which is just 

 perceptible is equal to about three-thousandths over the greater part 

 of the ordinary musical range. The ear perceives octaves as some- 

 what similar sounds. With these and other facts of hearing in 



