Wall effects on sound propagation in tubes

Numerical solutions have been obtained for the exact equations describing the propagation of periodic axisymmetric waves in a rigid cylindrical tube. Results were obtained for air over a range of conditions corresponding to shear wave numbers (s = R √ρ{variant}ω/μ) from 0·2 to 5000 and reduced frequencies (k = ωR/a) from 0·01 to 6. For conciseness and convenient application, the results for the attenuation and phase shift coefficients are given in the form of simple polynomials for the ranges 5 ≤ s ≤ 5000 and 0·01 ≤ k ≤ 6. This range covers virtually all values of tube diameter and sound frequency likely to be met in practical situations that are consistent with a continuum gas model