We experimentally study the spectral properties of a mixed system using the
flexural modes of a clover shaped plate. The system is called mixed becaus
e the corresponding ray dynamics has both chaotic and integrable regions in
its phase space. The eigenvalue statistics show intermediate properties be
tween the universal statistics corresponding to chaotic geometries which sh
ow Gaussian orthogonal ensemble statistics and integrable geometries that s
how Poisson statistics. We further investigate the Fourier transform of the
peaks to study the influence of the length scales of the plate on the prop
erties of the acoustic resonances. We observe a weak signal of the periodic
orbits in the experimental data. Although some of the peaks in the Fourier
transform of the eigenvalue spectrum correspond to the shortest stable per
iodic orbits, other strong peaks are also observed. To understand the role
of symmetries, we start with a clover shaped plate belonging to the C-4 ups
ilon point symmetry group, and progressively reduce the symmetry by sanding
one of the edges. A Shnirelman peak in P(s) is observed for the highly sym
metric situation due to level clustering.