Theoretical Analysis of Damping Due to Air Viscosity in Narrow Acoustic Tubes
Headphones and earphones have many extremely small
holes or narrow slits; they use sound-absorbing or porous material (i.e.,
dampers) to suppress vibratory system resonance. The air viscosity in
these acoustic paths greatly affects the acoustic properties. Simulation
analyses such as the finite element method (FEM) therefore require
knowledge of the material properties of sound-absorbing or porous
materials, such as the characteristic impedance and propagation
constant. The transfer function method using acoustic tubes is a widely
known measuring method, but there is no literature on taking
measurements up to the audible range. To measure the acoustic
properties at high-range frequencies, the acoustic tubes that form the
measuring device need to be narrowed, and the distance between the
two microphones needs to be reduced. However, when the tubes are
narrowed, the characteristic impedance drops below the air impedance.
In this study, we considered the effect of air viscosity in an acoustical
tube, introduced a theoretical formula for this effect in the form of
complex density and complex sonic velocity, and verified the
theoretical formula. We also conducted an experiment and observed
the effect from air viscosity in the actual measurements.
[1] M. A. Biot, Acoustics, Elasticity, and Thermodynamics of Porous Media.
Woodbury, New York: Acoustical Society of America, 1992.
[2] M. A. Biot, "Theory of propagation of elastic waves in a fluid-saturated
porous solid II: Higher frequency range," Journal of the Acoustical
Society of America, vol. 28, pp. 179-191,1956.
[3] H. Utsuno, Ting W. Wu, and A. F. Seybert " Prediction of Sound Fields in
Cavities with Sound Absorbing Materials", AIAA Journal, vol.28-11,
pp1870-1875, 1990.
[4] H. Utsuno, T. Tanaka, T. Fujikawa "Transfer function method for
measuring characteristic impedance and propagation constant of porous
materials", Journal of the Acoustical Society of America, vol. 86-2, pp.
637-643,1989.
[5] J. F. Allard and N. Atalla, Propagation of Sound in Porous Media. West
Sussex, UK: John Wiley & Sons, Ltd., 2009.
[1] M. A. Biot, Acoustics, Elasticity, and Thermodynamics of Porous Media.
Woodbury, New York: Acoustical Society of America, 1992.
[2] M. A. Biot, "Theory of propagation of elastic waves in a fluid-saturated
porous solid II: Higher frequency range," Journal of the Acoustical
Society of America, vol. 28, pp. 179-191,1956.
[3] H. Utsuno, Ting W. Wu, and A. F. Seybert " Prediction of Sound Fields in
Cavities with Sound Absorbing Materials", AIAA Journal, vol.28-11,
pp1870-1875, 1990.
[4] H. Utsuno, T. Tanaka, T. Fujikawa "Transfer function method for
measuring characteristic impedance and propagation constant of porous
materials", Journal of the Acoustical Society of America, vol. 86-2, pp.
637-643,1989.
[5] J. F. Allard and N. Atalla, Propagation of Sound in Porous Media. West
Sussex, UK: John Wiley & Sons, Ltd., 2009.
@article{"International Journal of Electrical, Electronic and Communication Sciences:64234", author = "M. Watanabe and T. Yamaguchi and M. Sasajima and Y. Kurosawa and Y. Koike", title = "Theoretical Analysis of Damping Due to Air Viscosity in Narrow Acoustic Tubes", abstract = "Headphones and earphones have many extremely small
holes or narrow slits; they use sound-absorbing or porous material (i.e.,
dampers) to suppress vibratory system resonance. The air viscosity in
these acoustic paths greatly affects the acoustic properties. Simulation
analyses such as the finite element method (FEM) therefore require
knowledge of the material properties of sound-absorbing or porous
materials, such as the characteristic impedance and propagation
constant. The transfer function method using acoustic tubes is a widely
known measuring method, but there is no literature on taking
measurements up to the audible range. To measure the acoustic
properties at high-range frequencies, the acoustic tubes that form the
measuring device need to be narrowed, and the distance between the
two microphones needs to be reduced. However, when the tubes are
narrowed, the characteristic impedance drops below the air impedance.
In this study, we considered the effect of air viscosity in an acoustical
tube, introduced a theoretical formula for this effect in the form of
complex density and complex sonic velocity, and verified the
theoretical formula. We also conducted an experiment and observed
the effect from air viscosity in the actual measurements.", keywords = "acoustic tube, air viscosity, earphones, FEM, porous material, sound-absorbing material, transfer function method", volume = "7", number = "6", pages = "781-5", }