Influence of the termination impedance on the eigen frequency
The eigenmodes of a system can be deducted from the analysis of the input impedance of a system
The input impedance of the system can be calculated with the help of the apparent impedance equation: by knowing the termination impedance
, the impedance
can be deduced.The continuity of pressure and volume velocity at the input leads to
.
Exemple :
Open ended tube
. In this case, the acoustical input impedance of the tube is written
where
is the length of the tube.
Tube open at
. In this case the input impedance is
. The condition
implies
, i.e.
. Knowing that
, the natural frequencies are given by
. The relation between tube length and wave length is
Tube closed at
. The condition
implies
, i.e.
. Knowing that
, the natural frequencies are given by
. The relation between tube length and wave length is
.
