Resonance of the Ear Canal (EAM) Resonance of the EAM approximates a uniform tube that is open at one end and closed at the other. Let’s assume for the moment that the EAM is a uniform tube (it’s not too far off). What would the FRC of this tube look like? Estimates vary, but the EAM in adults averages about 2.3 cm in length. f = c/λ (f=frequency in Hz; c=speed of sound=35,000 cm/s; λ=tube length ) F1 = c/4L (1 st formant=35,000/4. tube_length)
To do on your own: Calculate the two lowest formants of the EAM. Show the FRC of the EAM. What, if anything, might these calculations have to do with the audibility curve? Turn this in at our next class meeting. (To check your calculations, see the discussion of this topic in the auditory physiology chapter.)
Figure 4-3. The ear canal and middle ear cavity. Reprinted from Denes and Pinson, The Speech Chain, 1993, W.H. Freeman & Co. Note: (1) the cone shape of the TM, (2) attachment of malleus on the middle ear side. Tympanic Membrane (ear drum)
chorda tympani (branch of the facial n (cranial n 7)
(Zemlin, 1968, Fig 6-25) pyramidal eminence tendon of the stapedius muscle Posterior surface
(Zemlin, 1968, Fig 6-27) Anterior surface cochleariform process (another pyramid) tendon of the tensor tympani muscle
(Zemlin, 1998, Fig 6-52) (Zemlin, 1998, Fig 6-53) Ossicles resting on a dime
The Area Trick F = ma E = F/A (pressure=force/area) So, pressure can be amplified w/out a change force by decreasing the area over which the force is delivered.
The Area Trick Effective area of T.M. = cm 2 Area of stapes footplate = cm 2 So, pressure will be amplified by a factor of 0.594/0.032 = 18.6 (i.e., pressure is 18.6 times greater at the footplate than the T.M.). What is this in dB? Which version of the dB formula? We’re amplifying pressure, not intensity. So, we want the pressure version (20 log 10 Em/Er), right?
The Area Trick This is simpler than you might be thinking. dB PressureAmplification = 20 log 10 (E TM /E footplate ) How much is pressure being amplified? 0.594/0.032=18.6 dB PressureAmplification = 20 log = 25.4 dB