Let
denote the time to propagate across the length of
the cone in one direction. As is well known [22], the reflectance
at the tip of an infinite cone is
for pressure waves. I.e., it
reflects like an open-ended cylinder. We ignore any absorption losses
propagating in the cone, so that the transfer function from the entrance of
the cone to the tip is
. Similarly, the transfer function from
the conical tip back to the entrance is also
. The complete
reflection transfer function from the entrance to the tip and back is then
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(C.152) |
We now want to interface the conical cap reflectance
to the
cylinder. Since this entails a change in taper angle, there will be
reflection and transmission filtering at the cylinder-cone junction given
by Eq.(C.151) and Eq.(C.152).
From inside the cylinder, immediately next to the cylinder-cone
junction shown in Fig.C.48, the reflectance of the conical cap is
readily derived from Fig.C.48b and Equations (C.151) and
(C.152) to be
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|
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(C.153) |
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(C.154) |
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(C.155) |