This paper describes a distributed wireless acoustic sensor network (WASN) platform called WHISPER that is capable of synchronous multichannel sampling at different spatial locations with a sampling clock whose relative jitter is less than 300 ns. The platform comprises up to four data acquisition modules with onboard computing capabilities, and that can form an ad-hoc Wi-Fi network allowing an additional processing module such as a laptop or a smartphone to be connected if needed. Each acquisition module holds four digital SPI microphones with a total of 16 microphones for the entire system. Wireless synchronization of the sampling on each platform is implemented using a separate wireless module operating in the 902-928 MHz ISM band. Usage of this system is demonstrated in a real-time application involving spatial sound filtering through a beamforming algorithm.