This paper considers the problem of tracking multiple wideband acoustic sources in three dimensional (3-D) space using a distributed acoustic vector sensor (AVS) array. Least square approaches have been proposed to fuse the DOA measurements and estimate the 3-D position. However, the performance of position estimation can be seriously degraded by inaccurate DOA estimates, and also multiple source localization is impossible unless the DOA estimates can be associated to each source correctly. In this paper, A random finite set (RFS) approach is developed to jointly detect and track multiple wideband acoustic sources. An RFS is able to characterize the randomness of the state process (i.e., the dynamics of source motion and the number of active sources) as well as the measurement process (i.e., source detections, false alarms and miss detections). Since deriving a closed-form solution does not exist for the multi-source probability density, a particle filtering approach is employed to arrive at a computationally tractable approximation of the RFS densities. Simulations in different tracking scenarios demonstrate the ability of the proposed approaches in multiple acoustic source detection and tracking.