  We develop the microscopic theory for the attenuation of out-of-plane phonons
in stressed flexible two-dimensional crystalline materials. We demonstrate that
the presence of nonzero tension strongly reduces the relative magnitude of the
attenuation and, consequently, results in parametrical narrowing of the
phononspectral line. We predict the specific power-law dependence of the
spectral-line width on temperature and tension. We speculate that suppression
of the phonon attenuation by nonzero tension might be responsible for high
quality factors of mechanical nanoresonators based on flexural two-dimensional
materials.
