Back to Kemp Acoustics Home
Next: Inductance method
Up: Projection at a discontinuity
Previous: Volume velocity
Contents
In polar coordinates equation (B.6) becomes

(B.15) 
Substituting in equation (2.48) for and
performing the integration with respect to gives:

(B.16) 
This is in the form of the standard integral from
equation (A.1) of appendix A. Substituting in
the variables: , ,
and
gives
When the evaluation is carried out the contribution when is zero giving:




(B.17) 
Now noticing from equation (A.2) that
and using the fact that is a zero of
the second term vanishes:

(B.18) 
Expressing this in terms of the ratio of the radii,
we
get

(B.19) 
hence we have proved equation (2.85).
The integration used to obtain the analytical expression for is
identical to that for except that the labels are interchanged for
surface 1 and surface 2. Interchanging and means that
will be replaced with
giving
.
Back to Kemp Acoustics Home
Next: Inductance method
Up: Projection at a discontinuity
Previous: Volume velocity
Contents
Jonathan Kemp
20030324