An expression has been derived for the pressure field due to a rigid piston
with a velocity amplitude of
on the surface of a baffle. Consider a uniform duct terminated in an
infinite baffle. The plane wave mode will have a velocity source
identical to that of the piston.
Recalling equation (2.27), the axial velocity due to the th
mode is given by the modal velocity amplitude multiplied by
that mode's transverse velocity profile
.
Replacing the piston velocity source in (3.3) with this velocity
distribution gives the total pressure field assuming
only the th mode is present to provide a velocity source on the surface
.

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