Examination of the Effect of Air Viscosity on Narrow Acoustic Tubes Using FEM Involving Complex Effective Density and Complex Bulk Modulus

Earphones and headphones, which are compact electro-acoustic transducers, tend to have a lot of acoustic absorption materials and porous materials known as dampers, which often have a large number of extremely small holes and narrow slits to inhibit the resonance of the vibrating system, because the air viscosity significantly affects the acoustic characteristics in such acoustic paths. In order to perform simulations using the finite element method (FEM), it is necessary to be aware of material characteristics such as the impedance and propagation constants of sound absorbing materials and porous materials. The transfer function is widely known as a measurement method for an acoustic tube with such physical properties, but literature describing the measurements at the upper limits of the audible range is yet to be found. The acoustic tube, which is a measurement instrument, must be made narrow, and the distance between the two sets of microphones must be shortened in order to take measurements of acoustic characteristics at higher frequencies. When such a tube is made narrow, however, the characteristic impedance has been observed to become lower than the impedance of air. This paper considers the cause of this phenomenon to be the effect of the air viscosity and describes an FEM analysis of an acoustic tube considering air viscosity to compare to the theoretical formula by including the effect of air viscosity in the theoretical formula for an acoustic tube.

• M. Watanabe
• T. Yamaguchi
• M. Sasajima
• Y. Kurosawa
• Y. Koike

• Acoustic tube
• air viscosity
• earphones
• FEM
• porous materials
• sound absorbing materials
• transfer function method.

[1] H. Utsuno, T. W. Wu., A. F. Seybert, and T. Tanaka, "Prediction of SoundFields in Cavities with Sound Absorbing Materials,” AIAA Journal,.28, no. 11, 1990, pp.1870-1875.
[2] Yamaguchi, T., Tsugawa, J., Enomoto, H., Kurosawa., Y., "Layout of Sound Absorbing Materials in 3D Rooms Using Contributions with Eigenvectrs as Weight Coefficients,” the Japan Society of Mechanical Engineers, C-74, pp. 2648–2654, 2008.
[3] Yamaguchi, T., Kurosawa., Y., Matsumura, S., "Damping Analysis of 3D Acoustic Fields Involving Sound Absorbing Materials Using FEM,” the Japan Society of Mechanical Engineers, C-68-665, 2002-1
[4] Leo L. Beranek, 1986, Acoustics, America, Amer Inst of Physics; Rev Sub edition (December 1986)
[5] M. A. Biot, Acoustics, Elasticity, and Thermodynamics of Porous Media, Woodbury, New York, Acoustical Society of America, 1992.
[6] 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 28, pp. 179–191.
[7] J. F. Allard and N. Atalla, Propagation of Sound in Porous Media, West Sussex, United Kingdom, John Wily & Sons, Ltd., 2009.