Inelastic scattering experiments probe the spectral functions of solids, revealing information about the speeds and damping of propagating modes like acoustic waves. These properties are linked to transport coefficients such as thermal conductivity and viscosity. To extract this information from the experiments, a theoretical framework is needed to relate the spectral functions to the material's properties. The dynamical structure factor, derived from hydrodynamic equations, characterizes mass density fluctuations. In monoatomic crystals, eight hydrodynamic modes exist, splitting into six acoustic modes and two diffusive modes (heat and vacancy conduction). Recent theoretical advancements have enabled the analytical and numerical calculation of the dynamic structure factor for perfect crystals. This internship aims to extend these calculations to crystals with vacancies. First, the dynamical structure factor will be computed analytically using hydrodynamic equations. Subsequently, a molecular dynamics simulation will be employed to obtain a numerical result, in order to validate the theoretical results.