  We show experimentally that in a supercooled liquid composed of molecules
with internal degrees of freedom the internal modes contribute to the frequency
dependent shear viscosity and damping of transverse phonons, which results in
an additional broadening of the transverse Brillouin lines. Earlier, only the
effect of internal modes on the frequency dependent bulk viscosity and damping
of longitudinal phonons was observed and explained theoretically in the limit
of weak coupling of internal degrees of freedom to translational motion. A new
theory is needed to describe this new effect. We also demonstrate, that the
contributions of structural relaxation and internal processes to the width of
the Brillouin lines can be separated by measurements under high pressure.
