The Goertzel Algorithm provides an efficient mechanism for tone detection in signal processing. However, on Wireless Sensor Network nodes, there is often not sufficient processing power to implement this using floating-point arithmetic, so fixed-point implementations are used. In this paper we compare the quality of the results for a typical audio application with different resolutions of fixed-point support using MATLAB. We also provide performance figures based on implementing this on a representative sensor node platform. Our results show that, for this application-space, 16-bit fixed-point arithmetic provides the best tradeoff of accuracy against performance. No previous work has addressed this specific aspect of implementating the Goertzel algorithm.