Small acoustic tubes: New approximations including isothermal and viscous effects a)

Algebraic expressions are given (in FORT•aAN format for convenient use) that accurately approximate the value of the per unit-length acoustic impedance of small tubes (radii less than • acoustic wavelength) including isothermal nd viscous effects. Their accuracy of typically 3% or better was obtained as a result of adding a shunt conductance t rm to the traditional approximations and including frequency-dependent multiplicative factors. The multiplieative factors are simple expressions for the real or imaginary terms, providing a factor of 40 increase in calculational speed over the full Bessel-function solution. Experimental verification is presented for various combinations ofsmall tubes and cavities relevant to hearing aid applications, and the differences between the present approximations and previous approximations are illustrated using a 1-mm-diam tube as an example. Normalized complex series impedance and shunt admittance, characteristic mpedance, time delay, and attenuation constant plots are provided as a reference utilizing the more nearly exact Bessel solution.