We calculate the electron contribution to the phonon damping in layered superconductor with nodes in the spectrum. In the long-wavelength limit this damping is gapless and quadratically depends on the momentum. Only the phonons propagating along some particular directions are damped. Being connected with the symmetry of the order parameter, the angular dependence of damping may be used for its identification, which is illustrated by examples. The phonon Kohn anomaly in the superconducting state of La_2-xSr_xCuO₄ is also discussed. We attribute its "fine structure" previously observed for the magnetic structure factor by Won and Maki to the presence of low-energy crossover scale.