An analysis is presented of the motion of a thin fiber, supported on each end, due to a sound wave that propagates in the direction perpendicular to its long axis. Predicted and measured results indicate that when fibers or hairs having a diameter measurably less than 1 μm are subjected to air-borne acoustic excitation, their motion can be a very reasonable approximation to that of the acoustic particle motion at frequencies spanning the audible range. For much of the audible range of frequencies resonant behavior due to reflections from the supports tends to be heavily damped so that the details of the boundary conditions do not play a significant role in determining the overall system response. Thin fibers are thus constrained to simply move with the surrounding medium. These results suggest that if the diameter or radius is chosen to be sufficiently small, incorporating a suitable transduction scheme to convert its mechanical motion into an electronic signal could lead to a sound sensor that very closely depicts the acoustic particle motion over a wide range of frequencies.

References

References
1.
Stokes
,
G. G.
,
1851
,
On the Effect of the Internal Friction of Fluids on the Motion of Pendulums
, Vol.
9
,
Pitt Press
,
Cambridge, UK
.
2.
Cox
,
R. G.
,
1970
, “
The Motion of Long Slender Bodies in a Viscous Fluid Part 1. General Theory
,”
J. Fluid Mech.
,
44
(
4
), pp.
791
810
.https://doi.org/10.1017/S002211207000215X
3.
Rosenhead
,
L.
,
1963
,
Laminar Boundary Layers: An Account of the Development, Structure, and Stability of Laminar Boundary Layers in Incompressible Fluids, Together With a Description of the Associated Experimental Techniques
,
Clarendon Press
, London.
4.
Huang
,
W.-X.
,
Shin
,
S. J.
, and
Sung
,
H. J.
,
2007
, “
Simulation of Flexible Filaments in a Uniform Flow by the Immersed Boundary Method
,”
J. Comput. Phys.
,
226
(
2
), pp.
2206
2228
.
5.
Tornberg
,
A.-K.
, and
Gustavsson
,
K.
,
2006
, “
A Numerical Method for Simulations of Rigid Fiber Suspensions
,”
J. Comput. Phys.
,
215
(
1
), pp.
172
196
.
6.
Tornberg
,
A.-K.
, and
Shelley
,
M. J.
,
2004
, “
Simulating the Dynamics and Interactions of Flexible Fibers in Stokes Flows
,”
J. Comput. Phys.
,
196
(
1
), pp.
8
40
.
7.
Götz
,
T.
,
2000
, “
Interactions of Fibers and Flow: Asymptotics, Theory and Numerics
,” Ph.D. thesis, Technical University of Kaiserslautern, Kaiserslautern, Germany.
8.
Shelley
,
M. J.
, and
Ueda
,
T.
,
2000
, “
The Stokesian Hydrodynamics of Flexing, Stretching Filaments
,”
Physica D: Nonlinear Phenom.
,
146
(
1
), pp.
221
245
.
9.
Bringley
,
T. T.
,
2008
, “
Analysis of the Immersed Boundary Method for Stokes Flow
,”
Ph.D. thesis
, New York University, New York.
10.
Humphrey
,
J. A.
,
Devarakonda
,
R.
,
Iglesias
,
I.
, and
Barth
,
F. G.
,
1993
, “
Dynamics of Arthropod Filiform Hairs—I: Mathematical Modelling of the Hair and Air Motions
,”
Philos. Trans. R. Soc. London B
,
340
(
1294
), pp.
423
444
.
11.
Bathellier
,
B.
,
Steinmann
,
T.
,
Barth
,
F. G.
, and
Casas
,
J.
,
2011
, “
Air Motion Sensing Hairs of Arthropods Detect High Frequencies at Near-Maximal Mechanical Efficiency
,”
J. R. Soc. Interface
,
9
(
71
), pp.
1131
1143
.
12.
Göpfert
,
M. C.
, and
Robert
,
D.
,
2000
, “
Nanometre–Range Acoustic Sensitivity in Male and Female Mosquitoes
,”
Proc. R. Soc. London B: Biol. Sci.
,
267
(
1442
), pp.
453
457
.
13.
Johnston
,
C
.,
1855
, “
Original Communications: Auditory Apparatus of the Culex Mosquito
,”
J. Cell Sci.
,
1
(
10
), pp.
97
102
.
14.
Gopfert
,
M. C.
, and
Robert
,
D.
,
2001
, “
Active Auditory Mechanics in Mosquitoes
,”
Proc. R. Soc. London B
,
268
(
1465
), pp.
333
339
.
15.
Nadrowski
,
B.
,
Effertz
,
T.
,
Senthilan
,
P. R.
, and
Göpfert
,
M. C.
,
2011
, “
Antennal Hearing in Insects–New Findings, New Questions
,”
Hear. Res.
,
273
(
1
), pp.
7
13
.
16.
Barth
,
F. G.
,
2002
, “
Spider Senses–Technical Perfection and Biology
,”
Zoology
,
105
(
4
), pp.
271
285
.
17.
Shamble
,
P. S.
,
Menda
,
G.
,
Golden
,
J. R.
,
Nitzany
,
E. I.
,
Walden
,
K.
,
Beatus
,
T.
,
Elias
,
D. O.
,
Cohen
,
I.
,
Miles
,
R. N.
, and
Hoy
,
R. R.
,
2016
, “
Airborne Acoustic Perception by a Jumping Spider
,”
Curr. Biol.
,
26
(
21
), pp.
2913
2920
.
18.
Julius
,
W.
, and
Olson
,
H. F.
,
1932
, “
Sound Pick-Up Device
,” RCA Corp., New York, U.S. Patent No.
1,892,645
.https://www.google.com/patents/US1892645
19.
Olson
,
H. F.
,
1937
, “
Acoustical Device
,” RCA Corp., New York, U.S. Patent No.
2,102,736
.https://www.google.com/patents/US2102736
20.
Olson
,
H. F.
,
1947
,
Elements of Acoustical Engineering
,
D. Van Nostrand Company
,
New York
.
21.
Tao
,
J.
, and
Yu
,
X. B.
,
2012
, “
Hair Flow Sensors: From Bio-Inspiration to Bio-Mimicking—A Review
,”
Smart Mater. Struct.
,
21
(
11
), p.
113001
.
22.
Droogendijk
,
H.
,
Casas
,
J.
,
Steinmann
,
T.
, and
Krijnen
,
G.
,
2014
, “
Performance Assessment of Bio-Inspired Systems: Flow Sensing MEMS Hairs
,”
Bioinspiration Biomimetics
,
10
(
1
), p.
016001
.
23.
de Bree
,
H.-E.
,
2003
, “
An Overview of Microflown Technologies
,”
Acta Acust. Acust.
,
89
(
1
), pp.
163
172
.https://research.utwente.nl/en/publications/an-overview-of-microflown-technologies
24.
Leslie
,
C.
,
Kendall
,
J.
, and
Jones
,
J.
,
1956
, “
Hydrophone for Measuring Particle Velocity
,”
J. Acoust. Soc. Am.
,
28
(
4
), pp.
711
715
.
25.
Karniadakis
,
G.
,
Beskok
,
A.
, and
Aluru
,
N.
,
2005
,
Microflows and Nanoflows: Fundamentals and Simulation
,
Springer
,
New York
, p.
123
.
26.
Liou
,
W. W.
, and
Fang
,
Y.
,
2006
,
Microfluid Mechanics: Principles and Modeling
, McGraw-Hill Professional, New York.
27.
Nassios
,
J.
, and
Sader
,
J. E.
,
2013
, “
High Frequency Oscillatory Flows in a Slightly Rarefied Gas According to the Boltzmann–BGK Equation
,”
J. Fluid Mech.
,
729
, pp.
1
46
.
28.
Miles
,
R.
, and
Bigelow
,
S.
,
1994
, “
Random Vibration of a Beam With a Stick-Slip End Condition
,”
J. Sound Vib.
,
169
(
4
), pp.
445
457
.
29.
Blue Barn Fiber
, 2017, “
Stainless Steel Fiber
,” Blue Barn Fiber, Gooding, ID, accessed Aug. 14, 2017, http://www.bluebarnfiber.com/Stainless-Steel-Fiber_p_71.html
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