Bill's comment on science museum demos reminded me of my favorite
dispersive acoustic phenomenon. If you are fortunate enough to live
where you can skate outdoors on natural ice, observe the sound which
comes through the ice from the hard slap of a hockey stick on the
ice a hundred meters or more away from you. The sound starts with
higher partials and descends with a "BEEEOOOUUUP" sort of chirp. The
farther one is from the source, the longer the duration of the chirp.
I live on a lake, and though we hear it rarely, the sound of a large
sheet of ice cracking under gravitational stress as the lake drains
from beneath the ice is the most awesome I know in nature.