Skip to main content

An Analysis of the Acoustic Input Impedance of the Ear

Journal of the Association for Research in Otolaryngology volume 14, pages 611–622 (2013)Cite this article

Abstract

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.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

43,34 €

Price includes VAT (Finland)
Tax calculation will be finalised during checkout.

FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5

Notes

  1. Equation 2 was derived by combining Eqs. 18, 17, and 12 from Kringlebotn, with a modicum of algebra, and using a trigonometric identity for the tangent function in terms of e.

  2. The impedance of the ear canal at the eardrum is a function of the radius of the ear canal.

References

  • Aibara R, Welsh J, Puria S, Goode R (2001) Human middle-ear sound transfer function and cochlear input impedance. Hear Res 152:100–109

    PubMed  Article  CAS  Google Scholar 

  • 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 44–51

    Chapter  Google Scholar 

  • Bekesy G (1960) Experiments in hearing. McGraw Hill, New York

    Google Scholar 

  • Benade A (1968) On the propagation of sound waves in a cylindrical conduit. J Acoust Soc Am 44:616–623

    Article  Google Scholar 

  • 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 87:1237–1247

    PubMed  Article  CAS  Google Scholar 

  • Coleman T, Li Y (1994) On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math Program 67:189–224

    Article  Google Scholar 

  • Farmer-Fedor B, Rabbitt R (2002) Acoustic intensity, impedance and reflection coefficient in the human ear canal. J Acoust Soc Am 112:600–620

    PubMed  Article  CAS  Google Scholar 

  • Henry P (1931) The tube effect in sound-velocity measurements. Proc Phys Soc 43:340–362

    Article  Google Scholar 

  • Huang G, Rosowski J, Puria S, Peake W (2000) Tests of some common assumptions of ear-canal acoustics in cats. J Acoust Soc Am 108:1147–1161

    Google Scholar 

  • Kaye G, Sherratt G (1933) The velocity of sound in gases in tubes. Proc R Soc A 141:123–143

    Article  CAS  Google Scholar 

  • Keefe D, Simmons J (2003) Energy transmittance predicts conductive hearing loss in older children and adults. J Acoust Soc Am 114:3217–3238

    PubMed  Article  Google Scholar 

  • Keefe D, Ling R, Bulen J (1992) Method to measure acoustic impedance and reflection coefficient. J Acoust Soc Am 91:470–485

    PubMed  Article  CAS  Google Scholar 

  • Kringlebotn M (1994) Acoustic impedance in the human ear canal. Scandanavian Audiology 23:65–71

    Google Scholar 

  • Kringlebotn M (1988) Network model for the human middle ear. Scand Audiol 17:75–85

    PubMed  Article  CAS  Google Scholar 

  • 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 96:2184–2209

    Google Scholar 

  • Margolis R, Saly G, Keefe D (1999) Wideband reflectance tympanometry in normal adults. J Acoust Soc Am 106:265–280

    Google Scholar 

  • Moller A (1961) Network model of the middle ear. J Acoust Soc Am 33:168–176

    Google Scholar 

  • Moller A (1965) An experimental study of the acoustic impedance of the middle ear and its transmission properties. Acta Oto-Laryngologica 60:129–149

    Google Scholar 

  • O’Connor K, Puria S (2008) Middle-ear circuit model parameters based on a population of human ears. J Acoust Soc Am 123:197–211

    PubMed  Article  Google Scholar 

  • Parent P, Allen J (2007) Wave model of the cat tympanic membrane. J Acoust Soc Am 122:918–931

    Google Scholar 

  • Rabinowitz W (1981) Measurement of the acoustic input immittance of the human ear. J Acoust Soc Am 70:1025–1035

    PubMed  Article  CAS  Google Scholar 

  • Shields F, Lee K, Wiley W (1965) Numerical solution for sound velocity and absorption in cylindrical tubes. J Acoust Soc Am 37:724–729

    Google Scholar 

  • Stinson M (1985) The spatial distribution of sound pressure within scaled replicas of the human ear canal. J Acoust Soc Am 78:1596–1602

    PubMed  Article  CAS  Google Scholar 

  • Stinson M (1990) Revision of estimates of acoustic energy reflectance at the human eardrum. J Acoust Soc Am 88:1773–1778

    PubMed  Article  CAS  Google Scholar 

  • Voss S, Allen J (1994) Measurement of acoustic impedance and reflectance in the human ear canal. J Acoust Soc Am 95:372–384

    PubMed  Article  CAS  Google Scholar 

  • Voss S, Rosowski J, Merchant S, Peake W (2000) Acoustic responses of the human middle ear. Hear Res 150:43–69

    PubMed  Article  CAS  Google Scholar 

  • Voss S, Horton N, Woodbury R, Sheffield K (2008) Sources of variability in reflectance measurements on normal cadaver ears. Ear Hear 29:651–665

    PubMed  Article  Google Scholar 

  • Weston D (1953) The theory of the propagation of plane sound waves in tubes. Proc Phys Soc B 66:695–709

    Article  Google Scholar 

  • Withnell R, Jeng P, Waldvogel K, Morgenstein K, Allen J (2009) An in-situ calibration for hearing thresholds. J Acoust Soc Am 125:1605–1611

    PubMed  Article  Google Scholar 

  • Zwislocki J (1962) Analysis of the middle-ear function. part i: Input impedance. J Acoust Soc Am 34:1514–1523

    Google Scholar 

  • Zwislocki J (1970) An acoustic coupler for earphone calibration (Tech. Rep. No. LSC-S-7). Syracuse University

Download references

Acknowledgments

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.

Author information

Affiliations

  1. Department of Speech and Hearing Sciences, Indiana University, Bloomington, IN, 47405, USA

    Robert H. Withnell & Lauren E. Gowdy

  2. Neuroscience Program, Indiana University, Bloomington, IN, 47405, USA

    Robert H. Withnell

  3. Department of Physics, Indiana University, Bloomington, IN, 47405, USA

    Robert H. Withnell

Authors
  1. Robert H. Withnell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lauren E. Gowdy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert H. Withnell.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Withnell, R.H., Gowdy, L.E. An Analysis of the Acoustic Input Impedance of the Ear. JARO 14, 611–622 (2013). https://doi.org/10.1007/s10162-013-0407-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10162-013-0407-y

Keywords

  • ear canal acoustics
  • input impedance