I : 3/ Sound and the Ear 13 



frequency limit at which one can hear. Of these, the threshold sound 

 pressure level is most precise, but even it is a statistical limit. If an 

 individual is presented with an acoustic pressure close to his threshold, 

 he will hear the tone sometimes and not at other times. It is customary 

 in tests of this nature to choose the halfway point where the subject 

 hears the tone 50 per cent of the time as the limit of hearing. 



The upper limit of hearing is an even less clear concept. As the 

 sound pressure level is raised towards 110 db, one becomes aware of 

 feeling the sound in the external ear. At a still higher sound pressure 

 level, perhaps 130 db, one begins to experience pain. If the sound 

 pressure level is raised to 145 db, the pain becomes very severe. It has 

 been shown in accidents due to carelessness that at sound pressure levels 

 of about 155-160 db the human eardrum is ruptured. (The eardrum 

 will eventually heal.) 



It is instructive to convert these sound pressure levels for eardrum 

 rupture to actual sound pressures. Recall that the sound pressure level 

 is defined by 



L = 20 log 10 (Plpo) 

 where p = 0.0002 dynes/cm 2 



If L = 160 db 



then log 10 p/p = 8 



or pfp = 10 8 



Hence p = 2 x 10 4 dynes/cm 2 



This is the root mean square acoustic pressure. The acoustic pressure 

 amplitude will be the V2 times greater for a pure tone. This gives an 

 acoustic pressure amplitude A of 



A = 3 x 10 4 dynes/cm 2 



The average atmospheric pressure is about 10 6 dynes/cm 2 , so that 160 db 

 may also be written 



A = 0.03 atm 



The sound pressure level at which the eardrum is ruptured puts an 

 upper limit on the loudness which one can hear. The low frequency 

 limit to hearing is due to a different type of phenomenon. It used to be 

 stated that the upper and the lower frequency limits of hearing were at 

 the frequencies where the thresholds of pain and hearing crossed. At 

 the low frequency end of the human hearing range, this does not seem to 

 be the case. Rather, the limit at about 30 cps is due to the inability to 

 identify tones or direction of frequency change. 



In the audible range, a person recognizes the direction in which a 

 frequency change occurs, provided it is sufficiently great. For example, 



