Open Access
Table 1
Summary of the different types of cutoff frequencies used in the current article.
| Equations | Name and description | |
|---|---|---|
|
(12) | The local cutoff frequency is the natural frequency of a T-cell with one hole flanked by two lengths of bore that are closed at their extremities. The cell can be either symmetric (Eq. (12)) or asymmetric (Eq. (27)). Because this is a local quantity, it has a corresponding cell index n that is omitted to lighten the notation. |
|
(26) | The characteristic frequency is the natural frequency of a Π-cell consisting of two toneholes separated by a length of bore. Because this is a local quantity, it has a corresponding cell index n that is omitted to lighten the notation. |
|
— | The global cutoff frequency is a global property of a lattice for which each element has exactly the same natural frequency, in which case  . It is only strictly valid for an infinite, lossless lattice, but it is a good approximation for a tonehole network with at least three open toneholes and is used for finite lattices in this article. |
|
(19) | The transition band is an approximation of the global cutoff derived from the reflection coefficient. It defines a frequency band over which the lattice appears to transition from below to above the cutoff frequency. |
A lattice is geometrically regular if every cell is geometrically identical. In this case every cell has the same  (and  ) and the lattice has a global cutoff  . This is not possible for a conical lattice because no two cells can be identical due to the taper of the bore. |
||
A lattice is acoustically regular if every cell has the same local cutoff  (and  ), resulting in a global cutoff  . Conical bores can be acoustically regular because the cross-section and chimney height of a tonehole can be modified to account for the changing cross-section of the main bore. |
||
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.