2013/11/18 by Rogério Jorge, R. Jorge, Jorge, Rogério
Engineering · Physics and Astronomy · #Acoustic Wave Phenomena Research #Experimental and Theoretical Physics Studies #physics.flu-dyn #quant-ph
paper · pdf · doi:10.48550/arxiv.1311.4238
4 pages, 4 figures
arxiv created 2013/11/18 · arxiv updated 2013/11/19
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.