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Acoustic wave propagation inside a semi-infinite rigid cylindrical waveguide is investigated. The fluid which is inviscid (with zero mean flow) is modeled using a nonlinear equation. A finite amplitude monochromatic wave propagates through the waveguide starting from the finite end. The objective of this work is to find the critical frequencies and conditions for which there is a possibility of weak shock wave formation. With this objective, the regular perturbation method is used to separate the linear and the nonlinear set of equations that describe the velocity potential. For all variables to be finite at the centerline of the cylinder, at first order, the Bessel function of the first kind is used. Due to the rigid boundary at the fluid structure interface, the solutions along the radial direction are found to be orthogonal. The Fourier-Bessel series is used to solve the second order nonlinear equations. The nonlinearity of the system generates higher order frequencies and wavenumbers. It is found that the plane wave interactions are resonant at all frequencies and all other modal interactions result mostly in a beating phenomenon and occasionally in resonances at certain critical frequencies.
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