Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
The velocity reflection coefficient seen at port
is defined as
![$\displaystyle \rho^v_i \isdef \left. \frac{v^{-}_i(n)}{v^{+}_i(n)} \right\vert _{v^{+}_j(n)=0, \forall j\neq i} \protect$](img4976.png) |
(F.38) |
Representing the outgoing velocity wave
as the
superposition of the reflected wave
plus the
transmitted waves from the other ports, we have
![$\displaystyle v^{-}_i(n) = \rho^v_i v^{+}_i + \sum_{j\neq i} \tau^v_{ji} v^{+}_j \protect$](img4979.png) |
(F.39) |
where
denotes the velocity transmission
coefficient from
port
to port
. Substituting Eq.(F.36) into
Eq.(F.37) yields
Equating like terms with Eq.(F.39) gives
Thus, the
th beta parameter is the velocity transmission
coefficient from
th port to any other port (besides the
th). To
convert the transmission coefficient from the
th port to the
reflection coefficient for that port, we simply subtract 1. These
relationships are specific to velocity waves at a series junction
(cf. Eq.(F.19)). They are exactly the dual of Equations (F.19-F.20)
for force waves at a parallel junction.
Next |
Prev |
Up |
Top
|
Index |
JOS Index |
JOS Pubs |
JOS Home |
Search
[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]