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Method for calculation of input impedance
We have presented the equations for the pressure and
axial velocity in a duct in terms of the unknowns and .
Now we define the left hand side (negative side) of a
waveguide of arbitrary crosssection as the input end and the right hand side
(positive side) as the output end. The waveguide is then approximated by a
series of uniform sections as shown in figure 2.8 (cylinders in
circular geometry and rectangular sections in rectangular geometry).
Figure 2.8:
Horn approximated by a series of cylinders

In plane wave acoustics the impedance is defined as the ratio of the acoustic
pressure and volume velocity. For the multimodal case we define the acoustic
impedance matrix, , as follows:

(2.95) 
so that

(2.96) 
and therefore is the factor of contribution to the pressure
amplitude of the th mode due to the volume velocity amplitude of the th
mode. The vectors and matrices are infinite but must be truncated before
numerical implementation.
Subsections
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Jonathan Kemp
20030324