  We present a model for nonlinear decay of the weak wave in three-dimensional
incompressible magnetohydrodynamic (MHD) turbulence. We show that the decay
rate is different for parallel and perpendicular waves. We provide a general
formula for arbitrarily directed waves and discuss particular limiting cases
known in the literature. We test our predictions with direct numerical
simulations of wave decay in three-dimensional MHD turbulence, and discuss the
influence of turbulent damping on the development of linear instabilities in
the interstellar medium and on other important astrophysical processes.
