Cylindrical Tubes
In the case of cylindrical tubes, the logarithmic derivative of the
area variation,
ln, is zero, and Eq.
(C.148)
reduces to the usual momentum conservation equation
encountered when deriving the wave equation for plane waves
[318,349,47]. The present case reduces to the
cylindrical case when

If we look at sinusoidal spatial waves,
and
, then
and
, and the condition
for cylindrical-wave behavior becomes
, i.e., the spatial
frequency of the wall variation must be much less than that of the
wave. Another way to say this is that the wall must be approximately
flat across a wavelength. This is true for smooth horns/bores at
sufficiently high wave frequencies.
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Scattering Filters at the Cylinder-Cone Junction
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Digital Simulation