1. Figure 4-1. The three functional subdivisions of the auditory system
Figure 4-1. The three functional subdivisions of the auditory system. Reprinted from Deutsch and Richards (1979).

2. Figure 4-2. The pinna or auricle
Figure 4-2. The pinna or auricle. (Reprinted from Zemlin, 1968, Fig 6-12)

3. (external auditory meatus)
ear canal
(external auditory meatus)
cartilage
bone
(Zemlin, 1968, Fig 6-13)

4. 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/4λ (1st formant=35,000/4 . tube_length)

5. 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, and help to answer the last question, see the discussion of this topic in the auditory physiology chapter.)

6. Tympanic Membrane (ear drum)
Note: (1) the cone shape of the TM, (2) the tilt, and (3) attachment of malleus on the middle ear side.
Figure 4-3. The ear canal and middle ear cavity. Reprinted from Denes and Pinson, The Speech Chain, 1993, W.H. Freeman & Co.

7. chorda tympani (branch of the facial nerve (cranial nerve 7)

8. radial fibers (circular fibers not shown)
radial fibers (circular fibers not shown)

11. medial (toward the middle of the head)
The tympanic cavity is (very roughly) shaped like a cube. A cube has six surfaces.
posterior
(toward the back of the head)
medial (toward the middle of the head)
superior
lateral
(away from the middle of the head) TM
anterior (toward the front of the head)
inferior (beneath the cube)

12. Medial surface facial nerve oval window stapes footplate
anular ligament
promontory
round window
(Zemlin, 1968, Fig 6-18)

13. Posterior surface pyramidal eminence tendon of the stapedius muscle
(Zemlin, 1968, Fig 6-25)

14. Anterior surface cochleariform process (another pyramid)
tendon of the tensor tympani muscle
(Zemlin, 1968, Fig 6-27)

15. Ossicles resting on a dime
(Zemlin, 1998, Fig 6-53)
(Zemlin, 1998, Fig 6-52)

18. 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.

19. The Area Trick Effective area of T.M. = 0.594 cm2
Area of stapes footplate = cm2
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 log10 Em/Er), right?

20. The Area Trick
This is simpler than you might be thinking.
dBPressureAmplification= 20 log10 (ETM/Efootplate)
How much is pressure being amplified?
TM/SFP=0.594/0.032=18.6 (SFP=stapes footplate area)
dBPressureAmplification= 20 log = 25.4 dB

22. dBPressureAmplification= 20 log10(1.3) ≈ 2.3 dB
So, force is being amplified by a factor of 1.3. All else being equal, if force is amplified by 1.3, pressure (force/area) is also amplified by a factor of 1.3.
What is this in dB?
Which version of the formula do we want? Since we’re talking about the amplification of pressure, we want the pressure version.
dBPressureAmplification= 20 log10(1.3) ≈ 2.3 dB

23. We lost about 30 dB at the air-fluid boundary
We lost about 30 dB at the air-fluid boundary. How much of this intensity loss did the area and lever tricks recover?
Area trick: 25.4
Lever trick:
Total: 27.7
This is quite a bit. Later you will learn about the 10 dB Loudness Rule: Your subjective sense of loudness doubles with every 10 dB increase in intensity. So, a ~30 dB increase in intensity corresponds to a subjective increase in loudness by a factor of ~8 (i.e., x2 for 10 dB, x4 for 20 dB, and x8 for 30 dB).

24. Bottom Line
The middle ear impedance matching function is a big deal.
It is thought to be the main (or maybe the only) reason that the middle ear exists in the first place.
Because of the middle ear, sound energy that enters the fluid-filled cochlea is nearly 30 dB more intense and almost 8 times louder.