Terahertz (THz) wave plays important roles in the research of material properties, the non-invasive human security check and the next generation wireless communication. The progress of the scientific and technological applications of THz wave is strongly dependent on the improvement of THz detectors. Here a novel THz wave detection scheme is proposed in which the THz radiation is detected by an audible microphone based on the photo-thermo-acoustic (PTA) effect in graphene foam. Thanks to the room-temperature broadband electromagnetic absorption characteristics of graphene foam and the fast heat transfer between graphene foam and ambient air, this detection method not only inherits the advantages of the photo-thermal THz detector such as room-temperature and full bandwidth, but also has a response time 3 orders of magnitude faster than the photo-thermal detector. Besides, no micro-antenna/electrode is required to fabricate in the graphene foam THz detector which greatly simplifies the detector design and decreases the fabrication cost. It concludes that the room-temperature, full-bandwidth, fast-speed (>= 10 kHz), and easy-to-fabricate THz detector developed in this work has superior comprehensive performances among both the commercial THz detectors and the detectors recently developed in laboratory.