In many envisioned mobile ad hoc networks, nodes are expected to periodically beacon to advertise their presence. In this way, they can receive messages addressed to them or participate in routing operations. Yet, these beacons leak information about the nodes and thus hamper their privacy. A classic remedy consists in each node making use of (certified) pseudonyms and changing its pseudonym in specific locations called mix zones. Of course, privacy is then higher if the pseudonyms are short-lived (i.e., nodes have a short distance-to-confusion), but pseudonyms can be costly, as they are usually obtained from an external authority. In this paper, we provide a detailed analytical evaluation of the age of pseudonyms based on differential equations. We corroborate this model by a set of simulations. This paper thus provides a detailed quantitative framework for selecting the parameters of a pseudonym-based privacy system in peer-to-peer wireless networks.