Recently, cognitive radio (CR) technology has emerged as a promising solution to alleviate the spectrum scarcity problem. CR technology allows an unlicensed user to exploit the frequency bands unused by licensed users in an opportunistic manner. However, there is a critical issue when unlicensed users change their operating frequencies in the licensed bands. When an unlicensed user changes its operating frequency from a high frequency to a low frequency during a spectrum handoff, its transmission coverage enlarges, which increases the probability of interference to licensed users. In addition, when the unlicensed user changes its operating frequency from a low frequency to a high frequency during a spectrum handoff, its transmission coverage shrinks, which leads to the possibility of connection failure between the transmitting pair. In this paper, an optimal scheme is proposed to select a new operating frequency when an unlicensed user changes its operating frequency. The optimal frequency is obtained by considering the trade-offs between the probability of interference to licensed users and the probability of successful transmissions as well as the end-to-end throughput in both single-hop and multi-hop scenarios. Results show that the optimal operating frequency selected using the proposed scheme achieves the highest value of the objective function. To the best of our knowledge, this is the first paper that investigates the optimal operating frequency selection that considers the impact of the frequency to the transmission coverage in CR networks.