  We report the experimental observation of a geometric phase for elastic waves
in a waveguide with helical shape. The setup reproduces the experiment by
Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937-940,
2471] that showed first evidence of a Berry phase, a geometric phase for
adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic
geometric phase has been reported in quantum mechanics. We have performed an
experiment to observe the polarization transport of classical elastic waves. In
a waveguide, these waves are polarized and dispersive. Whereas the wavelength
is of the same order of magnitude as the helix's radius, no frequency dependent
correction is necessary to account for the theoretical prediction. This shows
that in this regime, the geometric phase results directly from geometry and not
from a correction to an adiabatic phase.
