4.7 Going Further: Calculating Input Impedance
199
Fig. 4.89 (continued)
where
Z
(ω) =
Z(ω)
Z c
=
Z(ω)S
ρc
(4.87)
is the normalised input impedance. Substituting Eq. 4.18 in Eq. 4.86 yields
Z
(ω) = j tan(kL) = j tan(ωL/c).
(4.88)
Equation 4.88, which is an explicit expression for the input impedance of the
tube, is described as an analytical solution for Z . Analytical solutions can be found
for a few geometries, including cylinders and cones, but not for the bores of realistic