To observe the complicated physical world, the sensors in a network sense and sample the data from the physical world. Currently, most existing works use the Equi-Frequency Sampling (EFS) methods or EFS based methods for data acquisition. However, the accuracy of EFS and EFS based methods cannot be guaranteed in practice since the physical world keeps changing continuously, and these methods do not effectively support reconstruction of the monitored physical world. To overcome the shortages of EFS and EFS based methods, this paper focuses on designing physical-world-aware data acquisition algorithms to support OðÞ-approximation to the physical world for any ! 0. Two physical-world-aware data acquisition algorithms are proposed. Both algorithms can adjust the sensing frequency automatically based on the changing trend of the physical world and the given . The thorough analysis on the performances of the algorithms are also provided. It is proven that the error bounds of the algorithms are OðÞ and the complexities of the algorithms are Oð 1 1=4 Þ. Based on the new data acquisition algorithms, an algorithm for reconstructing the physical world is proposed and analyzed. The theoretical analysis and experimental results show that the proposed algorithms have high performances on the aspects of accuracy and energy consumption.Index Terms-Wireless sensor networks, data acquisition Ç 1 MOTIVATION W IRELESS sensor networks (WSNs) are extremely important in cyber-physical systems (CPS) for observing and cognizing the complicated physical world at low cost. To observe the physical world by a WSN, the sensors in a WSN sense and sample the data from the physical world. Most of the current works use a simple equi-frequency sampling (EFS) method, in which each sensor senses and samples data from the physical world with equi-frequency. Based on EFS, many energy efficient data computation algorithms were proposed for WSNs, including the data collection algorithms [2], [3], [4], [5], the data query processing algorithms [6], [7], [8], [9], the data compression algorithms [10], [11], [12], the data mining and analyzing algorithms [13], [14], etc.However, since EFS only samples some discrete data points with a fixed frequency from the continuously-varying physical world, it may overlook some critical data and lead to distortion of the observed physical world when the sampling frequency is low, which results in misunderstanding of the physical world. To see the problem of EFS, we have performed an experiment to monitor wind velocity during 100 hours in the city of Harbin in China. The experimental results are presented in Fig. 1. Fig. 1a shows the curve for the real wind velocity, and other ones show the curve generated by the EFS method. As shown in Figs. 1b and 1c, many important values, such as maximal, minimal and inflection points are missed by EFS when the sampling frequency is not large enough. In addition, they also indicate that the distortion introduced by the EFS method becomes more obvious when the monitored physical worl...