Introduction to Acoustics

a)
b) ⎜pV/pT ⎜(dB)
40
20
0
0
–20
–40
10
1
0.1
0.01
0.03
0.001
0.03
ATM
Lever and
area ratio
model
LM
c) ⎜vS/pT ⎜(dB re 1 nS)
0.1 0.3 1 3 10 30
Human
Cat
Cat
–60
0.03
d) aEOW (cm
0.1 0.3 1 3 10 30
2 )
Cat
0.1 0.3 1 3 10 30
Frequency (kHz)
LI
AOW
Human
Fig. 12.3d [12.2]. This figure plots the effective area of
the ear as a sound collector as in Fig. 12.2c, except now
it refers to the sound power delivered to the oval win-
Physiological Acoustics 12.1 The External and Middle Ear 433
Fig. 12.3 (a) Schematic drawing of the mammalian middle
ear from the eardrum (TM on the left) to the oval window
(OW on the right). The malleus, incus, and stapes are shown
in their approximate anatomical arrangement. The areas of
the TM and OW are shown along with the lever arms of the
malleus (LM) andincus(LI). These lever arms are drawn
as if the malleus and incus rotate in the plane of the paper
around an axis indicated by the white dot. In reality, the
motion is more complex. (b) Ratio of the sound pressure
in scala vestibuli (pV) to the sound pressure at the eardrum
(pT) as a function of frequency, from measurements by Décory
(unpublished doctoral thesis, 1989 [12.2]). The dashed
line is the prediction of the model in (a) for typical dimensions
of the cat middle ear. (c) Transfer admittance of the
middle ear in human and cat, given as the velocity at the
stapes (vS) divided by the pressure at the eardrum (pT).
(d) Performance of the external and middle ears in sound
collection plotted as the effective area of the ear, referenced
to the oval window. This is the cross-sectional area across
which the ear collects sound power in a diffuse sound field,
plotted against frequency; the shaded bar shows the range
of cross sectional areas of the oval window for comparison.
Comparing with Fig. 12.2c shows the effect of the middle
ear. (After [12.2])
dow. Again, the dashed line shows the performance of
an ideal spherical receiver and is the same line as in
Fig. 12.2c. The effective area has a bandpass shape, as
in Fig. 12.2c, with a maximum at 3 kHz. The sharp drop
off in performance below 3 kHz was seen in the external
ear analysis and occurs because energy is not absorbed
at the eardrum at low frequencies. At higher frequencies
the effective area tracks the ideal receiver, but is about
10–15 dB smaller than the performance at the eardrum,
which approximates the ideal for the cat. This decrease
reflects the losses in the middle ear discussed above.
Although the external and middle ear do not approach
ideal performance, they do serve to couple sound into
the cochlea. As a comparison to the effective area in
Fig. 12.3d, the cross-sectional area of the oval window
is about 0.01–0.03 cm 2 in the cat and human (shaded
bar). Thus the effective area is larger than the area of
the oval window over the mid frequencies. Moreover, if
there were no middle ear, the collecting cross section of
the oval window would be smaller by about 15–30 dB
because of the impedance mismatch between the air and
cochlear fluids [12.19].
Part D 12.1