Wireless sensor network technologies have attracted a lot of attention in recent years. In this paper, we propose an energy-efficient data gathering mechanism using traveling wave and spatial interpolation for wireless sensor networks. In our proposed mechanism, sensor nodes schedule their message transmission timing in a fully-distributed manner such that they can gather sensor data over a whole wireless sensor network and transmit that data to a sink node while switching between a sleep state and an active state. In addition, each sensor node determines the redundancy of its sensor data according to received messages so that only necessary sensor data are gathered and transmitted to the sink node. Our proposed mechanism does not require additional control messages and enables both data traffic and control traffic to be drastically reduced. Through simulation experiments, we confirmed that with our proposed mechanism, the number of message transmissions can be reduced by up to 77% and the amount of transmitted data can be reduced by up to 13% compared to a conventional mechanism.