  We investigated experimentally and theoretically sound attenuation in the
quantum spin system TlCuCl_3 in magnetic fields at low temperatures. Near the
point of Bose-Einstein condensation (BEC) of magnons a sharp peak in the sound
attenuation is observed. The peak demonstrates a hysteresis as function of the
magnetic field pointing to a first-order contribution to the transition. The
sound damping has a Drude-like form arising as a result of hardcore
magnon-magnon collisions. The strength of the coupling between lattice and
magnons is estimated from the experimental data. The puzzling relationship
between the transition temperature and the concentration of magnons is
explained by their "relativistic" dispersion.
