Frequency Graphs
These graphs show the main frequency and the overtones when G is played on a D whistle. You can see the effects of the three different fipple materials.  Copper, with the highest peaks for all three overtones has the brightest sound.  Having different materials vibrating against each other causes some overtones to be damped with the other materials, resulting in a more mellow sound.
Copper:
Delrin:
Lucite: