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. Keywords—acoustic tube, air viscosity, earphones, FEM, porous material, sound-absorbing material, transfer function method