The wave offering could be eaten not only by the priests but by the priests’ sons and daughters in a ceremonially clean place. The intention of eating in a clean place is that the partaker of the meat should eat with inner cleanness, not simply in a place that is clean.
14 But the breast that is waved and the thigh that is contributed you shall eat in a clean place, you and your sons and your daughters with you, for they are given as your due and your sons’ due from the sacrifices of the peace offerings of the people of Israel.