  Sound attenuation in low temperature amorphous solids originates from their
disordered structure. However, its detailed mechanism is still being debated.
Here we analyze sound attenuation starting directly from the microscopic
equations of motion. We derive an exact expression for the zero-temperature
sound damping coefficient. We verify that the sound damping coefficients
calculated from our expression agree very well with results from independent
simulations of sound attenuation. The small wavevector analysis of our
expression shows that sound attenuation is primarily determined by the
non-affine displacements' contribution to the sound wave propagation
coefficient coming from the frequency shell of the sound wave. Our expression
involves only quantities that pertain to solids' static configurations. It can
be used to evaluate the low temperature sound damping coefficients without
directly simulating sound attenuation.
