  We discuss a random matrix model of systems with an approximate symmetry and
present the spectral fluctuation statistics and eigenvector characteristics for
the model. An acoustic resonator like, e.g., an aluminium plate may have an
approximate symmetry. We have measured the frequency spectrum and the widths
for acoustic resonances in thin aluminium plates, cut in the shape of the
so-called three-leaf clover. Due to the mirror symmetry through the middle
plane of the plate, each resonance of the plate belongs to one of two mode
classes and we show how to separate the modes into these two classes using
their measured widths. We compare the spectral statistics of each mode class
with results for the Gaussian orthogonal ensemble. By cutting a slit of
increasing depth on one face of the plate, we gradually break the mirror
symmetry and study the transition that takes place as the two classes are
mixed. Presenting the spectral fluctuation statistics and the distribution of
widths for the resonances, we find that this transition is well described by
the random matrix model.
