I wish I could be more specific, but a reed with a shallot or
a free reed produces anything but a sine wave.  In fact, the free
reed produces all kinds of harmonics, and the beating reed, when
it snaps closed, gives sharp peaks.

I cannot recall seeing a reed pipe without some kind of adjustment
to the resonator.  Tuning a reed pipe is a balancing act between the
reed adjustment (beating reed) and the resonator and tuning can be
quite frustrating.

Pipe construction is covered very thoroughly in Volume II of Audsley's
book, "The Art of Organ-Building", Dover Publications.  A good
library should be able to find a copy.

Bill Chapman - in record breaking heat,
Palm Springs, California