We were doing the standard standing-waves-on-a-string experiment with a physical science class yesterday. The students decided to have an extra long (>2 m) string. They found a fundamental mode (a single "loop") at 8 Hz. They doubled the frequency to 16 Hz and found a single loop, not 2. Increasing to 24 Hz produced 3 loops. Going to 32 Hz, back to 2 loops. 40 Hz produced 5 loops. 48 Hz produced 3 loops. It looks like a double fundamental.
My best guess (strictly a guess) is: 1) the string is a "bungee" string which has a fabric sheath around an elastic core, 2) the length increases the possibility of non-linear or co-linear effects. One component (the elastic core by itself?) has a fundamental, and the combined string has another, and the length allows the bifurcation. I haven't measured the mass/length of the components, but will do that.
Anybody else see this before? (A friend commented that J. Denker probably has a paper already written up about this. :) )