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Open Quantum Systems Decoherence

Nonlinear Acoustics - Perturbation Theory and Webster's Equation

arXiv

Authors: Rogério Jorge

Year

2013

Paper ID

31873

Status

Preprint

Abstract Read

~2 min

Abstract Words

121

Citations

N/A

Abstract

Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schrödinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.

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This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1311.4238 [2] arXiv https://arxiv.org/abs/1311.4238 [3] Publisher https://arxiv.org/abs/1311.4238

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