One of the critical issues in a sensor network concerns the detection of changes in data streams. Recently presented change detection schemes primarily use a sliding window model to detect changes. In such a model, a distance function is used to compare two sliding windows. Therefore, the performance of the change detection scheme is greatly influenced by the distance function. With regard to sensor nodes, however, energy consumption constitutes a critical design concern because the change detection scheme is implemented in a sensor node, which is a small battery-powered device. In this paper, we present a comparative study of various distance functions in terms of execution time, energy consumption, and detecting accuracy through simulation of speech signal data. The simulation result demonstrates that the Euclidean distance function has the highest performance while consuming a low amount of power. We believe our work is the first attempt to undertake a comparative study of distance functions in terms of execution time, energy consumption, and accuracy detection.