Wireless sensor networks can provide a cheap and flexible infrastructure to support the measurement of noise pollution. However, the processing of the gathered data is challenging to implement on resource-constrained nodes, because each node has its own limited power supply, low-performance and low-power micro-controller unit and other limited processing resources, as well as limited amount of memory. We propose a sensor node for monitoring of indoor ambient noise. The sensor node is based on a hardware platform with limited computational resources and utilizes a number of simplifications to approximate more complex and costly signal processing stage. Furthermore, to reduce the communication between the sensor node and a sink node, as well as the power consumed by the IEEE 802.15.4 (ZigBee) transceiver, we perform digital A-weighting filtering and non-calibrated calculation of the sound pressure level on the node. According to experimental results, the proposed sound level meter can accurately measure the noise levels of up to 100~dB, with the mean difference of less than 2~dB compared to Class 1 sound level meter. The proposed device can continuously monitor indoor noise for several days. Despite the limitations of the used hardware platform, the presented node is a promising low-cost and low-power solution for indoor ambient noise monitoring.