Physics:Duct modes

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

[math]\displaystyle{ p = \sum \alpha_i \phi_i }[/math]

where [math]\displaystyle{ \alpha_i }[/math] is the participation factor or modal amplitude and [math]\displaystyle{ \phi_i }[/math] is the mode shape. The duct mode shape are analytically determined from the solution of the Helmholtz equation.