An Analysis of the Acoustic Input Impedance of the Ear

  • Robert H. WithnellEmail author
  • Lauren E. Gowdy
Research Article


Ear canal acoustics was examined using a one-dimensional lossy transmission line with a distributed load impedance to model the ear. The acoustic input impedance of the ear was derived from sound pressure measurements in the ear canal of healthy human ears. A nonlinear least squares fit of the model to data generated estimates for ear canal radius, ear canal length, and quantified the resistance that would produce transmission losses. Derivation of ear canal radius has application to quantifying the impedance mismatch at the eardrum between the ear canal and the middle ear. The length of the ear canal was found, in general, to be longer than the length derived from the one-quarter wavelength standing wave frequency, consistent with the middle ear being mass-controlled at the standing wave frequency. Viscothermal losses in the ear canal, in some cases, may exceed that attributable to a smooth rigid wall. Resistance in the middle ear was found to contribute significantly to the total resistance. In effect, this analysis “reverse engineers” physical parameters of the ear from sound pressure measurements in the ear canal.


ear canal acoustics input impedance 



Robert Withnell is indebted to the School of Mechanical Engineering at The University of Western Australia for generously hosting his sabbatical and for the award of a Gledden Senior Research Fellowship that provided the impetus for this work. Doug Keefe, Mead Killion, and one anonymous reviewer, provided valuable feedback and advice on earlier versions of this paper. Portions of this paper were presented at the Mechanics of Hearing 2011 conference in Williamstown, MA, USA and the American Auditory Society conference in Scottsdale, AZ, USA.


  1. Aibara R, Welsh J, Puria S, Goode R (2001) Human middle-ear sound transfer function and cochlear input impedance. Hear Res 152:100–109PubMedCrossRefGoogle Scholar
  2. Allen J (1986) Measurement of eardrum acoustic impedance. In: Allen JB, Hall JL, Hubbard A, Neely ST, Tubis A (eds) Peripheral auditory mechanisms. Springer, New York, pp 44–51CrossRefGoogle Scholar
  3. Bekesy G (1960) Experiments in hearing. McGraw Hill, New YorkGoogle Scholar
  4. Benade A (1968) On the propagation of sound waves in a cylindrical conduit. J Acoust Soc Am 44:616–623CrossRefGoogle Scholar
  5. Chan J, Geisler C (1990) Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal. J Acoust Soc Am 87:1237–1247PubMedCrossRefGoogle Scholar
  6. Coleman T, Li Y (1994) On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math Program 67:189–224CrossRefGoogle Scholar
  7. Farmer-Fedor B, Rabbitt R (2002) Acoustic intensity, impedance and reflection coefficient in the human ear canal. J Acoust Soc Am 112:600–620PubMedCrossRefGoogle Scholar
  8. Henry P (1931) The tube effect in sound-velocity measurements. Proc Phys Soc 43:340–362CrossRefGoogle Scholar
  9. Huang G, Rosowski J, Puria S, Peake W (2000) Tests of some common assumptions of ear-canal acoustics in cats. J Acoust Soc Am 108:1147–1161Google Scholar
  10. Kaye G, Sherratt G (1933) The velocity of sound in gases in tubes. Proc R Soc A 141:123–143CrossRefGoogle Scholar
  11. Keefe D, Simmons J (2003) Energy transmittance predicts conductive hearing loss in older children and adults. J Acoust Soc Am 114:3217–3238PubMedCrossRefGoogle Scholar
  12. Keefe D, Ling R, Bulen J (1992) Method to measure acoustic impedance and reflection coefficient. J Acoust Soc Am 91:470–485PubMedCrossRefGoogle Scholar
  13. Kringlebotn M (1994) Acoustic impedance in the human ear canal. Scandanavian Audiology 23:65–71Google Scholar
  14. Kringlebotn M (1988) Network model for the human middle ear. Scand Audiol 17:75–85PubMedCrossRefGoogle Scholar
  15. Lynch T, Peake W, Rosowski J (1994) Measurements of the acoustic input impedance of cat ears: 10 hz to 20 khz. J Acoust Soc Am 96:2184–2209Google Scholar
  16. Margolis R, Saly G, Keefe D (1999) Wideband reflectance tympanometry in normal adults. J Acoust Soc Am 106:265–280Google Scholar
  17. Moller A (1961) Network model of the middle ear. J Acoust Soc Am 33:168–176Google Scholar
  18. Moller A (1965) An experimental study of the acoustic impedance of the middle ear and its transmission properties. Acta Oto-Laryngologica 60:129–149Google Scholar
  19. O’Connor K, Puria S (2008) Middle-ear circuit model parameters based on a population of human ears. J Acoust Soc Am 123:197–211PubMedCrossRefGoogle Scholar
  20. Parent P, Allen J (2007) Wave model of the cat tympanic membrane. J Acoust Soc Am 122:918–931Google Scholar
  21. Rabinowitz W (1981) Measurement of the acoustic input immittance of the human ear. J Acoust Soc Am 70:1025–1035PubMedCrossRefGoogle Scholar
  22. Shields F, Lee K, Wiley W (1965) Numerical solution for sound velocity and absorption in cylindrical tubes. J Acoust Soc Am 37:724–729Google Scholar
  23. Stinson M (1985) The spatial distribution of sound pressure within scaled replicas of the human ear canal. J Acoust Soc Am 78:1596–1602PubMedCrossRefGoogle Scholar
  24. Stinson M (1990) Revision of estimates of acoustic energy reflectance at the human eardrum. J Acoust Soc Am 88:1773–1778PubMedCrossRefGoogle Scholar
  25. Voss S, Allen J (1994) Measurement of acoustic impedance and reflectance in the human ear canal. J Acoust Soc Am 95:372–384PubMedCrossRefGoogle Scholar
  26. Voss S, Rosowski J, Merchant S, Peake W (2000) Acoustic responses of the human middle ear. Hear Res 150:43–69PubMedCrossRefGoogle Scholar
  27. Voss S, Horton N, Woodbury R, Sheffield K (2008) Sources of variability in reflectance measurements on normal cadaver ears. Ear Hear 29:651–665PubMedCrossRefGoogle Scholar
  28. Weston D (1953) The theory of the propagation of plane sound waves in tubes. Proc Phys Soc B 66:695–709CrossRefGoogle Scholar
  29. Withnell R, Jeng P, Waldvogel K, Morgenstein K, Allen J (2009) An in-situ calibration for hearing thresholds. J Acoust Soc Am 125:1605–1611PubMedCrossRefGoogle Scholar
  30. Zwislocki J (1962) Analysis of the middle-ear function. part i: Input impedance. J Acoust Soc Am 34:1514–1523Google Scholar
  31. Zwislocki J (1970) An acoustic coupler for earphone calibration (Tech. Rep. No. LSC-S-7). Syracuse UniversityGoogle Scholar

Copyright information

© Association for Research in Otolaryngology 2013

Authors and Affiliations

  1. 1.Department of Speech and Hearing SciencesIndiana UniversityBloomingtonUSA
  2. 2.Neuroscience ProgramIndiana UniversityBloomingtonUSA
  3. 3.Department of PhysicsIndiana UniversityBloomingtonUSA

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