Physics:Duct modes

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The acoustic pressure in a cylindrical duct can be expressed as the superposition of duct modes:

$p=\sum {\alpha }_i{\varphi }_i$

where ${\alpha }_i$ is the participation factor or modal amplitude and ${\varphi }_i$ is the mode shape. The duct mode shape are analytically determined from the solution of the Helmholtz equation.