20 Sound and the Ear /I : 4 



measurements, variations of ± 10 per cent from the mean are quite 

 usual but variations as great as ± 20 per cent are rare. The meatus 

 is terminated by a thick fibrous membrane called the tympanum or tym- 

 panic membrane. Along the edges of the membrane are glands which 

 secrete a waxlike substance called cerumen. This forms a protective 

 coating. In cases of irritation, an excess of this wax is secreted, often 

 causing a temporary loss of hearing. 



The external auditory meatus may be thought of somewhat as a 

 closed-end organ pipe. The tympanum at the end of the meatus is 

 relatively stiff. Here, the particle velocity should be a minimum and 

 the acoustic pressure a maximum. The opening to the air should be 

 just the opposite, a pressure node and particle velocity antinode. The 

 diagram in Figure 4 shows that the external auditory meatus at reson- 

 ance is a quarter wavelength long. At this frequency, about 3 kc, there 

 will be a maximum acoustic pressure delivered to the inner ear for a 

 given incident pressure. This resonance corresponds to the minimum 

 in the pure tone threshold curve. Studies with probe tubes attached to 

 microphones show that the maximum pressure amplification in the ear 

 canal is about 10 db. This is not sufficient to account for the threshold 

 minimum from 1-4 kc but definitely contributes to it. 



At the base of the external auditory meatus is the tympanic membrane. 

 In humans it is oval in shape, about 66 mm 2 in area and about 0.1 mm 

 thick. It couples the vibration of the air molecules in the outer ear 

 to the small bones of the middle ear. At extreme intensities the tym- 

 panic membrane is a nonlinear device; that is, it produces harmonics 

 and subharmonics of the frequencies exciting it. These nonlinear effects 

 however are only important at very high sound pressure levels. In 

 some mammalian species, the tympanum vibrates as an elastic mem- 

 brane. In other species including the human, the motion of the tym- 

 panum is more like that of a rotating piston. The mode of vibration of 

 the tympanum was studied in detail by von Bekesy. 



Various techniques have been used to observe the motion of the 

 tympanum. The simplest is to glue a long light stick to the tympanum 

 and observe the motion of the end of the stick. Most of these techniques 

 are useful only at low frequencies; the results can be extended only by 

 extrapolation. Tests of this type show that the particle velocity of the 

 tympanum is of the same order of magnitude as that in a plane wave in 

 air. Applying this result to db, the approximate threshold at 1 kc, 

 one finds for the particle velocity v 



P 



v = — 



pc 

 v = 5 x 10 ~ 6 cm/sec 



