  An thin elastic steel plate is excited with a vibrator and its local velocity
displays a turbulent-like Fourier spectrum. This system is believed to develop
elastic wave turbulence. We analyze here the motion of the plate with a
two-point measurement in order to check, in our real system, a few hypotheses
required for the Zakharov theory of weak turbulence to apply. We show that the
motion of the plate is indeed a superposition of bending waves following the
theoretical dispersion relation of the linear wave equation. The nonlinearities
seem to efficiently break the coherence of the waves so that no modal structure
is observed. Several hypotheses of the weak turbulence theory seem to be
verified, but nevertheless the theoretical predictions for the wave spectrum
are not verified experimentally.
