Using frequency hopping for fair resources allocation in TV white spaces is proposed and evaluated in this paper. The degree of fairness is judged by the achieved throughput by different secondary users. The throughput of the secondary users is determined by their permissible transmission power and the interference from the TV and other secondary users. The permissible transmission power for secondary users in TV white spaces in different channels is investigated. The main concern of calculating the permissible secondary user transmission power is protecting the primary TV receivers from harmful interference. With the aid of SPLAT (RF Signal Propagation, Loss, And Terrain analysis tool), the received TV signal power in a study case of the surroundings of the city of Gävle is fetched. The interference from the TV transmission into the free channels is measured in six different locations. The simulated system is a deployed Wi-Fi access points in a building representing an office environment in an urban area. Moreover, the size of the hopping set and the number of APs influences are investigated.