Not yet reviewed by Pith; the record is open.

Theoretical calculations of sound-wave velocities of materials at extreme conditions are of great importance to various fields, in particular geophysics. For example, the seismic data on sound-wave propagation through the solid iron-rich Earth's inner core have been the main source for elucidating its properties and building models. As the laboratory experiments at very high temperatures and pressures are non-trivial, ab initio predictions are invaluable. The latter, however, tend to disagree with experiment. We notice that many attempts to calculate sound-wave velocities of matter at extreme conditions in the framework of quantum-mechanics based methods have not been taking into account the effect of anharmonic atomic vibrations. We show how anharmonic effects can be incorporated into ab initio calculations and demonstrate that in particular they might be non-negligible for iron in Earth's core. Therefore, we open an avenue to reconcile experiment and ab initio theory.