English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Webster's horn equation (1919) offers a one-dimensional approximation forlow-frequency sound waves along a rigid tube with a variable cross-sectionalarea. It can be thought as a wave equation with a source term that takes intoaccount the nonlinear geometry of the tube. In this document we derive thisequation using a simplified fluid model of an ideal gas. By a simple change ofvariables, we convert it to a Schr\"odinger equation and use the well-knownvariational and perturbative methods to seek perturbative solutions. As anexample, we apply these methods to the Gabriel's Horn geometry, deriving thefirst order corrections to the linear frequency. An algorithm to the harmonicmodes in any order for a general horn geometry is derived.

Nonlinear Acoustics -- Perturbation Theory and Webster's Equation