Sound transmission across a smooth nonuniform section in an infinitely long duct

Sound transmission across a nonuniform section in an infinite duct is studied numerically using the finite element method. An impedance matched absorptive portion is added to each end of the computational domain so as to avoid the undesirable higher mode reflection that will otherwise take place there. Results suggest that the sound fields downstream of the nonuniform section inlet are complicated and cannot be easily described by the conventional solution of the wave equation. The distribution of acoustic energy among the various propagating modes well downstream from the outlet of the nonuniform section is also discussed. Results show that the first symmetrical higher mode is important for all cases. The plane wave becomes important at high frequency with high rate of change of the cross-sectional area when the section is a convergent one.