We propose to study the vibrational dynamics and the anharmonicity effects of the orthorhombic ZnSb by time of flight spectroscopy. ZnSb is a promising thermoelectric material with thermal conductivity as low as in the skutterudite compounds. In a previous experiment, we have find a peak at about 5 meV in the phonon density of states corresponding to low energy optic modes, in good agreement with our ab initio calculations. However, due to too small wavevector and temperature range that can be investigated with the IN6 TOF spectrometer, we were not able to study quantitatively neither the wave-vector dependence of the phonon density of states, indispensable to understand the vibrational dynamics and its relation with structure motifs such as Sb2 dumbbells, nor its temperature dependence that could permit to study quantitatively the anharmonicity. This is the purpose of the present continuation proposal to carry such study by use of the TOF IN4 spectrometer. The present study could have large impact on the search of thermoelectric materials in confirming that umklapp scattering of acoustic phonons by low energy optic mode can happen in compounds without atoms intercalated in cages.