Duct modes

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

${\displaystyle p=\sum \alpha _{i}\phi _{i}}$

where ${\displaystyle \alpha _{i}}$ is the participation factor or modal amplitude and ${\displaystyle \phi _{i}}$ is the mode shape. The duct mode shape are analytically determined from the solution of the Helmholtz equation.^[1]

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