In more complex geometries where thermal and viscous losses are important, see The Thermoviscous Acoustics, Frequency Domain Interface, which is more fundamental and detailed.
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The wide duct approximation can be used for any duct cross section in the limit where the duct width is significantly larger than the acoustic boundary layer thickness. See Wide Ducts.
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The very narrow circular ducts (isothermal) can only be used when the duct width is so small that isothermal conditions apply. This is when the duct width is much smaller than the acoustic thermal boundary layer thickness. See Very Narrow Circular Ducts (Isothermal).
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The slit, circular duct, rectangular duct, and equilateral triangular duct models are based on an analytical solution of the thermoviscous acoustic equations in the limit where the acoustic wavelength is much larger than both the duct cross section (below the cut-off frequency) and the boundary layer thickness. This is the case in most engineering applications. See Slits, Circular Ducts, Rectangular Ducts, and Equilateral triangular Ducts.
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Finally, selecting the user defined option enables you to enter expressions for the complex wave number and the complex acoustic impedance. These may be analytical expressions, interpolated values, or values extracted from a detailed boundary mode analysis using the full formulation of The Thermoviscous Acoustics, Boundary Mode Interface.
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To determine the complex propagation constants for a waveguide, of arbitrary cross section, use The Thermoviscous Acoustics, Boundary Mode Interface. Apply it on the cross-section geometry of the waveguide. The interface solves for the propagating modes and includes all losses in detail. The complex wave number kc is then given by the plane wave mode solved for. This is the variable tabm.kn. The predefined variable tabm.Zc gives the (lumped) complex characteristic impedance Zc. Search for the mode nearest to the (lossless) plane wave mode.
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