Lumped elements
Définition :
The hypotheses used are called the lumped element hypotheses. These are true when the wavelength is very large relative to the greatest dimension of an object. In the case of a duct of length L, they are mathematically expressed by
, where
is the wavenumber, and
, where
is the wavelength.
Exemple :
Example 1: for a 10 cm long tube, the low frequencies are in the 0 - 3000 Hz range.
Example 2: for a 1 m long tube, the low frequencies are in the 0 - 300 Hz range.
Complément :
Consequences
The problem under study is unidimensional, the wavefront is planar.
The physical quantities have a linear variation between the input and output of the tube. The partial derivatives can be written as finite differences.
Thus, only the physical quantities at the input and output of the tube are considered (and not at every point of the tube like when the wavelength is smaller than the dimensions of the duct).
