Reflection from a non-uniform acoustic waveguide with fitted rigid rings using a Transfer Function method

Abstract

An acoustic waveguide consisting of a cylindrical tube with fitted thin rigid rings whose inner radius decreases appropriately causes incident acoustic waves to slow down, resulting in considerable absorption in the cavities between the rings. The absorption becomes greater towards the end of the waveguide, where the wave speed becomes very small and the waves are spatially concentrated. Such a system demonstrates the so-called ‘Acoustic Black Hole’ effect. In this paper, the reflection coefficient of an acoustic waveguide whose ring inner radius has either a linear or a quadratic profile is calculated, using a Transfer Function method. A Transmission Line model is also used, which forms a low-frequency approximation to the Transfer Function method. Different geometrical assumptions for the cavity between two consecutive rings and for the core of the waveguide are considered for both methods. The results are compared with experimental ones from the literature. The numerical results
predict the general characteristics of the reflection coefficient. For the linear case, the fluctuations of the reflection coefficient are also predicted over part of the spectrum.

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