The sensor and the smartphone app combined have a latency of only 24ms. Note: Bluetooth speakers and bluetooth headphones add big latencies. When audio cables are used, the latency is low. Check this list for low-latency portable speakers on the market. Analog Hifi-Systems have almost no latency.
It can reach your mobile device until 7 meters straight distance. The condition depends on the smartphone/tablet performance. Other wireless devices might interfere the connection. If used inside or in spaces with walls and ceilings the range goes up to 30m.