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acoustic admittance acoustic field Admittance from finite-element aeroacoustic aNY,NY axial propagation constant Beckemeyer boundary condition boundary layer boundary value problem centerline Mach number coefficient matrices coordinate system eigenvalue problem equa equation 18 equation 25 equation 30 equation and boundary exact values Excellent comparison Figure finite-element method flow impedance test flow impedance tube flow profile governing the acoustic grazing flow impedance grazing-flow impedance tube impedance test laboratory integration Langley Research Center linear matrix mean-flow profile measurements NASA node normal particle velocity number of points numerical method NY+1 O.OOi obtained ONE-DIMENSIONAL SHEARED FLOW paper parameters partial differential equation particle displacement Rectangular Duct restricted sample calculation scheme SHEARED FLOW Admittance single cross-sectional direction solution to equation solved sound pressure level sound-absorbing specified test sample test specimen tion two-dimensional sheared flow uniform flow unknown admittance value upper wall eigenfunction value problem vector wall admittance wall pressure eigenfunction wave number z-direction zero flow