Explicit approximation of the wavenumber for lined ducts
Résumé
For acoustic waves in lined ducts, at given frequencies, the dispersion relation leads to a transcendental equation for the wavenum-ber that has to be solved by numerical methods. Based on Eckart explicit expression initially derived for water waves, accurate explicit approximations are proposed for the wavenumber of the fundamental mode in lined ducts. While Eckart expression is 5 % accurate, some improved approximations can reach maximum relative error of less than 10 −8. The cases with small dissipation part in the admittance of the liner and/or axisymmetric ducts are also considered.
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