A Mathematical Model of Fluid Dynamics in the Ear due to External Noise
Keywords:
Noise, Cochlea, Potential Theory, Fluid Motion, HearingAbstract
COMMUNICATION IN PHYSICAL SCIENCES 5(1): 59-69
C. E. Mbah
A mathematical model offluid dynanücs in the Cochlea was fornudated and solved using the potential flow theory. The obtained solutions of the model representing the flow in the Cochlea shows that the flow looks chaotic, but in reality, it is so because ofthe nudti-dimensional nature of the variables associated with noise. Also determined is the nature ofthe flow at both chambers of the cochlea where we saw that the magnitudes of the velocity potentials are the same with only a difference in sign denoting their positions in relation to the basilar Inenlbrane. We observed that the velocity potential in the horizontal axis increases with distance front the base of the basilar 'nembrane when the flexural rigidity varies as the distance increases. Other analyses were also carried out to confinn the experimental evidences about the effect ofnoise in the ear.
Downloads
References
Thesis at the University of Nigeria, Nsukka. 2005.
Barbel, Hen-nberger; Stefan Kempf and Gunter Ehret: Basic Maps in the auditory Stefan Kempf Midbrain: Bio. Lynbern. 87, Gunter Ehret 231- 240, Springer-Verlag 2002.
Barrett, L. C. & Wylie, C. R. : Advanced Engineering Mathematics. McGraw Hill Book Company, New York. 1995
Bell, J & Holmes, M.H. (1986b): Modeling auditory nerve response due to strain activated transduction mechanism. In conf. Proc. of the twelfth Winter congress. Acoustics Toronto Can.
Burtons, G & Hopkin J.W: Understanding Biology. Harcourt Brace, Jovanovich Inc. New York, 1983
Chalupnik, J.D.: Transportation noise: In a symposium on acceptability criteria, Michigan. Ann Arbor Science publisher Inc.
, 1977
Cheremisionoff, P.N. & Cheremisionoff, P.P. Industrial noise control book, Michigan, Ann Arbor Science publisher Inc. 9, 1978
Goblick, J.J & Pfeiffer, R.R (1969): Time domain measurements of cochlea nonlinearities using combination click stimuli. J Acoust. Soc. Am. 46, 124.
Golstein, J. L. (1967): Auditory non-linearity. J. Acoust. Soc. Am. 41, 76
Green, A.E. & Naghdi, P.M. (1967): Micro polar and director theories of plates. Quart. Mech. Appl. Math.26, 183-202.
Gupta, B. D.: Mathematical Physics, Viskas Pub. House, Prt, Ltd India, 1987.
Harold, T. D. : Introduction to Non-linear differential equations. Dover pub. Inc. NY. 1982
Lamb, H (1904): On deep-water waves. Proceeding of the London Math. Soc. Series 2, 2, 371-400
Lesser, M. B. and Berkley, D.A. (1972): Fluid Mechanic of the Cochlea Part I. J. Fluid Mech. 51, 3, 497-512
Lzsser, M. B. and Berkley, D.A. (1976): A Simple Mathematical Model of the Cochlea, Proc. 7th Am. S. E. S. meeting (ed A.C. Eringen), Reprinted
Morse, P. M.: Vibration and sound, Second edition, New York, McGraw-Hill Ltd, 1948
Pain, H. S.: The Physics of vibrations and waves, 2nd edition, John Wiley and Sons Ltd, London, 1976.
Ranke, O. F. (1950b): Theory of Operation of the Cochlea. J. Acoust. soc. Am. 22, 772777
Rau, J.G. & Woolen, D. C. : Environmental impact analysis handbook, New York and London, McGraw-Hill, 1980
Rhode, W. S. (1971): Observations on the •vibration of the basilar membrane in squirrel monkeys using the mosbaur technique. J. Acoust. Soc. Am. 49, 1218-1231
Titchmarch, E. C.: The theory of functions, Oxford University Press, Second Edition, New York. 1986
Von Bekesy (1947): The vibration phase along the basilar membrane with sinusoidal variation, J. Acoust. Soc. Am. 19, 452-460
Wegel, G.; Reisz, R. K. & Blackman, R. B. (1932): Low frequency thresholds of hearing and of feeling in the ear and ear mechanism J. Acoust. Soc. Am. 4, 6.
Wever, E. G. & Lawrence, M. (1930b); The transmission properties of the Stapes. Ann. otol. Rhinol. Laryngol. 59, 322-330
Wever, E. G. & l*wrence, M. (1930b); The transmission properties of the middle ear. Ann. Otol. Rhinol. Laryngol. 59, 5-18.
Downloads
Published
Issue
Section
License
Copyright (c) 2010 The Journal and the author
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.