Cutoff Frequencies and Evanescent Modes
Possible solutions for the axial factor in the Helmholtz equation are
A propagating guided wave is described by
For a given frequency, the modes are limited for
Evanescent modes, do not transport acoustic energy down the duct.
If the frequency is greater than the cutoff , the mode is propagating
If the frequency is less than the cutoff then the mode is evanescent
For all propagating modes other than a plane wave, propagation above the
cut-off frequency the is dispersive
Possible solutions for the axial factor in the Helmholtz equation are
A propagating guided wave is described by
For a given frequency, the modes are limited for
Evanescent modes, do not transport acoustic energy down the duct.
If the frequency is greater than the cutoff , the mode is propagating
If the frequency is less than the cutoff then the mode is evanescent
For all propagating modes other than a plane wave, propagation above the
cut-off frequency the is dispersive
Guided wave modes describes sound waves in a duct
Cross Sectional Eignefunctions
Solutions of the Helmholtz equation may be constructed using
separation-of-variables yielding
introduction of the separation constant leads to the following differential
equations
For ducts with rectangular cross sections the eigenfunctions and
eigenvalues can be describes as
Cross Sectional Eignefunctions
Solutions of the Helmholtz equation may be constructed using
separation-of-variables yielding
introduction of the separation constant leads to the following differential
equations
For ducts with rectangular cross sections the eigenfunctions and
eigenvalues can be describes as
