The cochlea is the most important part of the hearing system, due to the fact that it transforms sound guided through air, bone, and lymphatic fluid to vibrations of the cochlear partition which includes the organ of Corti with its sensory cells. These send nerve impulses to the brain leading to hearing perception. The work presents the wave propagation in rigid ducts filled with air or water including viscous-thermal boundary layer damping. In extension, a mechanical box model of the human cochlea represented by a rectangular duct limited by the tapered basilar membrane at one side is developed and evaluated numerically by the finite element method. The results match with rare experiments on human temporal bones without using the physically unfounded assumption of Rayleigh damping. A forecast on the concept of the traveling wave parametric amplification is given to potentially explain the high hearing sensitivity and otoacoustic emissions.

References

1.
Helmholtz
,
H. V.
,
1860
, “
Theorie der Luftschwingungen in Röhren mit offenen Enden
,”
J. Reine Angew. Math.
,
LVII
(
1
), pp.
1
72
.
2.
Kirchhoff
,
G.
,
1868
, “
Über den Einfluss der Wärmeleitung in einem Gase auf die Schallbewegung
,”
Poggendorfer Ann.
,
210
(6), pp.
177
193
.
3.
Rayleigh
,
L.
,
1896
,
Theory of Sound II
, 2nd ed.,
Macmillan
,
London
, pp.
319
326
.
4.
Prandtl
,
L.
,
1904
‚ “
Über Flüssigkeitsbewegung bei sehr kleiner Reibung
,” Verhandlungen des III Internationalen Mathematiker-Kongresses, Heidelberg, Germany, pp.
484
491
.
5.
Kampinga
,
R.
,
2010
, “
Viscothermal Acoustics Using Finite Elements—Analysis Tools for Engineers
,”
Ph.D. thesis
, University of Twente, Enschede, The Netherlands.
6.
Schlichting
,
H.
,
1982
,
Grenzschicht-Theorie
,
Verlag G. Braun
,
Karlsruhe, Germany
, pp.
1
843
.
7.
Sommerfeld
,
A.
,
1908
, “
Ein Beitrag zur hydrodynamischen Erklärung der Turbulenten Flüsigkeitsbewegungen
,”
Fourth International Mathematical Congress Rome Accademia Lincei
, Rome, Italy, Apr. 6–11, Vol.
3
, pp.
116
124
.
8.
Bogert
,
B. P.
,
1951
, “
Determination of the Effects of Dissipation in the Cochlear Partition by Means of a Network Representing the Basilar Membrane
,”
J. Acoust. Soc. Am.
,
23
(
2
), pp.
151
154
.
9.
Steele
,
C. R.
,
1974
, “
Behavior of the Basilar Membrane With Pure-Tone Excitation
,”
J. Acoust. Soc. Am.
,
55
(
1
), pp.
148
162
.
10.
Kim
,
D. O.
,
1973
, “
A System of Nonlinear Differential Equations Modeling Basilar-Membrane Motion
,”
J. Acoust. Soc. Am.
,
54
(
6
), pp.
1517
1529
.
11.
Ramamoorthy
,
S.
,
Zha
,
D. J.
, and
Nuttall
,
A. L.
,
2010
, “
The Biophysical Origin of Traveling-Wave Dispersion in the Cochlea
,”
Biophys. J.
,
99
(
6
), pp.
1687
1695
.
12.
Li
,
Y.
, and
Grosh
,
K.
,
2012
, “
Direction of Wave Propagation in the Cochlea for Internally Excited Basilar Membrane
,”
J. Acoust. Soc. Am.
,
131
(
6
), pp.
4710
4721
.
13.
Gold
,
T.
, and
Pumphrey
,
R. J.
,
1948
, “
Hearing—I: The Cochlea as a Frequency Analyzer
,”
Proc. R. Soc. B
,
135
(
881
), pp.
462
491
.
14.
Kemp
,
D. T.
,
1978
, “
Stimulated Acoustic Emissions From the Human Auditory System
,”
J. Acoust. Soc. Am.
,
64
(
5
), pp.
1386
1391
.
15.
Rayleigh
,
L.
,
1883
, “
On Maintained Vibrations
,”
Philos. Mag. Ser. 5
,
15
(
94
), pp.
229
235
.
16.
Epstein
,
P. S.
, and
Carhart
,
R. S.
,
1953
, “
The Absorption of Sound in Suspensions and Emulsions
,”
J. Acoust. Soc. Am.
,
25
(
3
), pp.
553
565
.
17.
Holmes
,
M. J.
,
Parker
,
N. G.
, and
Povey
,
M. J. W.
,
2011
, “
Temperature Dependence of Bulk Viscosity in Water Using Acoustic Spectroscopy
,”
J. Phys.: Conf. Ser.
,
269
, p. 012011.
18.
Stokes
,
G. G.
,
1845
, “
On the Theories of the Internal Friction of Fluids in Motion and of the Equilibrium and Motion of Elastic Solids
,”
Trans. Cambridge Philos. Soc.
,
8
, pp.
287
305
.
19.
Davis
,
C. M.
, and
Litovitz
,
T. A.
,
1965
, “
Two-State Theory of the Structure of Water
,”
J. Chem. Phys.
,
42
(
7
), pp.
2563
2576
.
20.
Pinkerton
,
J. M. M.
,
1947
, “
A Pulse Method for the Measurement of Ultrasonic Absorption in Liquids: Results for Water
,”
Nature
,
160
(
4056
), pp.
128
129
.
21.
Bossart
,
R.
,
Joly
,
N.
, and
Bruneau
,
M.
,
2003
, “
Hybrid Numerical and Analytical Solutions for Acoustic Boundary Problems in Thermo-Viscous Fluid
,”
J. Sound Vib.
,
263
(
1
), pp.
69
84
.
22.
ANSYS
,
2015
, “
ANSYS Release 17.1 Software Documentation
,” ANSYS, Inc., Canonsburg, PA.
23.
Hannink
,
M. H. C.
,
2004
, “
Optimized Sound Absorbing Trim Panels for the Reduction of Aircraft Cabin Noise
,” 11th International Congress on Sound and Vibration (
ICSV 11
), St. Petersburg, Russia, July 5–8, pp. 1855–1862.
24.
Böhnke
,
F.
,
Semmelbauer
,
S.
, and
Marquardt
,
T.
,
2015
, “
Influence of Young's Moduli in 3D Fluid-Structure Coupled Models of the Human Cochlea
,”
AIP Conference Proceedings
,
1703
(1), p.
070013
.
25.
Lempriere
,
B. M.
,
1968
, “
Poisson's Ratio in Orthotropic Materials
,”
AIAA J.
,
6
(
11
), pp.
2226
2227
.
26.
Morse
,
P. M.
, and
Ingard
,
K. U.
,
1986
,
Theoretical Acoustics
,
Princeton University Press
,
Princeton, NJ
, pp.
1
927
.
27.
Bruneau
,
M.
,
1998
,
Manuel d'Acoustique Fondamentale
,
Editions Hermes
,
Paris, France
.
28.
Huxley
,
A. F.
,
1969
, “
Is Resonance Possible in the Cochlea After All?
,”
Nature
,
221
(
8
), pp.
935
940
.
29.
Békésy
,
G.
,
1949
, “
On the Resonance Curve and the Decay Period at Various Points on the Cochlear Partition
,”
J. Acoust. Soc. Am.
,
21
(
3
), pp.
245
254
.
30.
Stenfelt
,
S.
,
2003
, “
Basilar Membrane and Osseous Spiral Lamina Motion With Air and Bone Conduction Stimuli
,”
Hear. Res.
,
181
(1–2), pp.
131
143
.
31.
Wang
,
Y.
,
Steele
,
C. R.
, and
Puria
,
S.
,
2016
, “
Cochlear Outer-Hair-Cell Power Generation and Viscous Fluid Loss
,”
Sci. Rep.
,
6
(
1
), p.
19475
.
32.
Elliott
,
S. J.
,
2007
, “
Wave Propagation in a Constrained Fluid Layer Bounded by an Elastic Half-Space and Its Relevance in Cochlear Micromechanics
,”
J. Sound Vib.
,
305
(4–5), pp.
918
924
.
33.
Freeman
,
D. M.
,
Abnet
,
C. C.
,
Hemmert
,
W.
,
Tsai
,
B. S.
, and
Weiss
,
T. F.
,
2003
, “
Dynamic Material Properties of the Tectorial Membrane: A Summary
,”
Hear. Res.
,
180
(1–2), pp.
1
10
.
34.
Heijden
,
M.
, and
Versteegh
,
C. P.
,
2015
, “
Energy Flux in the Cochlea: Evidence Against Power Amplification of the Traveling Wave
,”
JARO
,
16
(
5
), pp.
581
597
.
35.
Cullen
,
A. L.
,
1959
, “
Theory of the Travelling-Wave Parametric Amplifier
,”
IEEE Proceedings
,
107
(32), pp.
101
107
.
36.
Batchelor
,
D. B.
,
1976
, “
Parametric Resonance of Systems With Time-Varying Dissipation
,”
Appl. Phys. Lett.
,
29
(
5
), pp.
280
281
.
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