A note on a WKB application to a duct of varying cross-section
type: Item
instance of: scholarly article
title: A note on a WKB application to a duct of varying cross-section
zbMATH Open document ID: 1021.76048
DOI: 10.1016/S0893-9659(01)80024-0
author: M. J. Crocker
author: Jorge P. Arenas
published in: Applied Mathematics Letters
publication date: 2002-06-13T00:00:00Z
review text: The authors study the two-dimensional problem of plane wave propagation of sound along a tube of gradually varying cross-sectional area. The classical equations of this problem are written. In the case of stationary medium, these equations yield the classical wave equation governing the sound pressure. The steady-state solution of this equation is converted to Liouville standard form: a differential equation of second order, with variable coefficients. Using the WKB method, the authors obtain an approximate harmonic solution for this differential equation, and give the impedance of a particular cosine-shaped horn terminated in an infinite baffle. The presented computation of normalized acoustic impedance shows less floating point operations when compared with the Runge-Kutta algorithm.
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 1755230
zbMATH Keywords: duct
zbMATH Keywords: varying cross-section
zbMATH Keywords: Liouville differential equation
zbMATH Keywords: plane wave propagation
zbMATH Keywords: wave equation
zbMATH Keywords: sound pressure
zbMATH Keywords: WKB method
zbMATH Keywords: approximate harmonic solution
zbMATH Keywords: cosine-shaped horn
zbMATH Keywords: normalized acoustic impedance
MaRDI profile type: Publication
cites work: Q5558293
cites work: Q4693794
full work available at URL: s0893-9659(01)80024-0
OpenAlex ID: W2034022758
description: scientific article; zbMATH DE number 1755230