The density of phonon states in the thermoelectric material Yb₁₄MnSb₁₁ has been studied first by inelastic neutron scattering and second in an element-specific way by nuclear inelastic x-ray scattering. The low sound velocity of 1880(50) m / s as obtained from the density of phonon states can be identified as an important reason for the low heat transport in this system. The high melting temperature of Yb₁₄MnSb₁₁ contrasts with the low energy of all phonons (Lattice dynamics in the thermoelectric Zintl compound Yb₁₄MnSb₁₁ contrasts  with th low nrgy od all phonons (< 25 meV) and relates to an unusual lack of softening of phonon modes with temperature, when comparing the phonon density of states observed at ambient temperatures and at 1200 K. We have also measured the density of phonon states of the related Eu₁₄MnSb₁₁ compound and of the thermoelectric Zintl phase Zn₄Sb₃ in order to compare with related thermodynamic properties of Yb₁₄MnSb₁₁ and to elucidate the different mechanisms of the heat conductivity reduction in Zintl phases.