Design of an energy efficient Wireless Sensor Network (WSN) has emerged as an important research area. Minimizing energy consumption is the primary objective for WSN. WSN is usually characterized by tiny size, low cost and low transmission power. So optimization of transmission power is of great importance. Optimal transmit power not only achieves better network lifetime but also reduces inter-node interference significantly. In this paper, the authors carry out simulation studies to investigate the effects of Rayleigh fading on the performance of WSN and optimal transmit power in presence of Rayleigh fading is derived.