Synchronizing data communication between nodes with energy efficiency by adapting different duty cycling mechanisms is the most important task of Medium Access Control (MAC) protocol in wireless sensor networks (WSNs). Most of the low-duty-cycle MAC protocols address the issue of unicast efficiently,ignoring the broadcast performance, which presents significant challenges due to the duty cycling. In this paper, we propose an asynchronous low-duty-cycle MAC protocol for broadcasts in WSN that incorporates the advantages of existing sender-initiated and receiver-initiated MAC protocols. The Preamble-Based Receiver-Initiated Broadcast MAC (PRIB-MAC) protocol is built on RI-MAC unicast MAC protocol by adding a preamble to support broadcasting. It is found that the duration of the preamble depends on the time difference in the wake-up schedule of the nodes and with an optimized wake-up schedule, the preamble duration of just 2% of the slot duration can give 100% node coverage in very less time compared with ADB: an efficient multi-hop broadcast protocol based on asynchronous duty cycling in WSNs.