Nuclear resonant inelastic x-ray scattering is used to measure the projected partial phonon density of states of materials. A relationship is derived between the low-energy part of this frequency distribution function and the sound velocity of materials. Our derivation is valid for harmonic solids with Debye-like low-frequency dynamics. This method of sound velocity determination is applied to elemental, composite, and impurity samples which are representative of a wide variety of both crystalline and noncrystalline materials. Advantages and limitations of this method are elucidated.PACS numbers: 61.10. Eq, 62.65.+k Mechanical properties form an important part of our understanding of condensed matter. In many areas of science, measurements of sound velocity are used to study materials of both natural occurence and artificial fabrications. For example, in the field of geophysics, the sound velocity is the most direct information we have about the Earth's interior. The standard approach to learn about the composition and structure of the Earth's interior entails measurements of sound velocities of candidate compounds. The results are then compared to seismological data to exclude or confirm a particular compound. In the following, we will describe the use of nuclear resonant inelastic x-ray scattering (NRIXS) to measure the velocity of sound.The NRIXS method was introduced to probe the lattice dynamics of materials by employing low-energy nuclear resonances.1,2 In NRIXS experiments, only signals from nuclear resonance absorption are monitored, and for this reason the extracted quantity is specific to the resonant isotope. This technique provides the phonon excitation spectrum as seen by the probe nuclei, 3,4,5 and in most cases one can extract the partial vibrational frequency distribution, a function often referred to as the partial phonon density of states (PDOS). The NRIXS method has been applied to various materials, e.g., thin films and multilayers, 19,20 Most of these samples are compounds, and, while the obtained PDOS gives only part of the lattice dynamics, the low-energy portion of the PDOS provides the Debye sound velocity of the whole sample. We will now show that, due to universal features of acoustic modes of harmonic solids, the low-energy portion of the PDOS is related to the Debye sound velocity in a simple way.The normalized phonon density of states is defined bywhere the energy eigenstates of lattice vibrations E l are labeled by quantum number l, and N is the total number of atoms in the solid. In the harmonic lattice approximation, a PDOS, which is more relevant to NRIXS experiments, is given bywhere ν enumerates resonant nuclei,Ñ is the total number of resonant nuclei,k is a unit vector in the incident photon direction, and e ν l are phonon polarization vectors. Equation (2) shows that the vibrational polarizations are projected onto the incident photon direction and in particular the vibrational modes with polarization perpendicular to the direction of the incident photon do not contribute...