Abstract
The paper presents derivation of the impedance matrix based on the rigorous solution of the wave equation obtained by the Wiener-Hopf technique for a semi-infinite unflanged cylindrical duct. The impedance matrix allows, in turn, calculate the acoustic impedance along the duct and, as a special case, the radiation impedance. The analysis is carried out for a multimode incident wave accounting for modes coupling on the duct outlet not only qualitatively but also quantitatively for a selected source operating inside. The quantitative evaluation of the acoustic impedance requires setting of modes amplitudes which has been obtained applying the mode decomposition method to the far-field pressure radiation measurements and theoretical formulae for single mode directivity characteristics for an unflanged duct. Calculation of the acoustic impedance for a non-uniform distribution of the sound pressure and the sound velocity on a duct cross section requires determination of the acoustic power transmitted along/radiated from a duct. In the paper, the impedance matrix, the power, and the acoustic impedance were derived as functions of Helmholtz number and distance from the outlet.
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