A wireless tandem alarm having a first alarm configured for physical connection to an industrial machine having an electronic machine controller, and a second alarm configured for detachable connection to the first alarm or to the industrial machine. Each alarm has a housing, a piezoelectric transducer within the housing, a processor configured to drive the piezoelectric transducer in response to a control signal, and a wireless transceiver configured for relatively short-range, low-power communications. In the first alarm, the processor drives the piezoelectric transducer in response to a signal from the machine controller and, also responsive to the machine controller signal, transmits a control signal via the wireless transceiver. In the second alarm, the wireless transceiver receives the control signal from the first alarm and supplies it to the processor, which is configured drive the piezoelectric transducer in response. The alarms are configured to work in tandem, when attached to each other, to cooperatively produce a combination of sound characteristics not achievable with either alarm alone. The alarms are also configured to detect when they are detached from each other and to respond by changing one or more sound characteristics. When detached, the alarms are also capable of affecting the operation of each other via two-way wireless communications.