## Acoustic Theory of Axisymmetric Multisectioned Ducts |

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### Contents

SUMMARY | 1 |

UNIFORM MULTISECTIONED DUCT FIG 5 | 15 |

Application to Circular Duct | 23 |

1 other sections not shown

### Common terms and phrases

Aa[jm Ab[jm acoustic admittances acoustic field acoustic modes acoustic treatment admittance discontinuity aircraft turbofan engine amplitude eq annular duct backward-moving wave boundary condition circular and annular circular duct continuity and momentum cylindrical coordinates dimensionless Dirac delta function duct section duct systems duct without flow eigenfunction equation 25 equation 39a equation 69 equations 17 equations are derived finite ducts flange Fourier transform Green's function hard-walled identity matrix infinite Langley Research Center m\iv matrix equations matrix formulation matrix notation mode amplitudes mode number mode reflection momentum equations multisection liners my.v noise source number of planes orthogonal problem radiation directivity factors radiation from ducts radiation patterns radiation reflection reflection coefficients reflection effects reflection equations reflection matrices scaled complex acoustic shown in figure submatrix subscripts and superscripts theory transmission and reflection unflanged duct uniform flow uniform liner uniform multisectioned duct vector w-j+k w+k-j w+k+j wall admittance wave amplitudes wave equation wave number