Conventionally there are two ways of approaching noise control engineering: either tackle the noise at source or use sound absorbent materials. In this dissertation, we extend experience of a third method, developed and demonstrated in the last ten years: active sound control. Active sound control techniques are developed for the reduction of the noise from a premixed, turbulent flame and the quietening of a flame-driven Rijke tube. In both cases the light emission of the flame, at an excited free radical wavelength, is crucial to our schemes since it gives a suitable measure of the noise to be reduced. Previous investigations into active sound control are reviewed, as is the previous work on flame noise, and from this literature review we find that: (i) the noise from compact flames is monopole and predominantly low frequency and this makes it amenable to the single degree-of-freedom active control methods developed (and successfully demonstrated) in this laboratory; (ii) there is a similarity between the light and sound emission properties of hydrocarbon flames, due to their connection with the heat release taking place at the flame front; (iii) digital active control is more versatile and successful than analogue methods. Consideration of these conclusions shows that the previous active control methods may be developed into a configuration which should attenuate flame noise. This configuration contains three nonideal stages wherein the control might fail: detecting the noise; antialiasing this control signal and processing it correctly in the digital filter. Separate chapters consider these topics so that the deterioration in the system performance due to each stage is kept to a minimum. Once the system is assembled in an experiment we find a lOdB reduction in the band 200-800Hz for a premixed, turbulent, ' propane/air flame. The idea of using the light emission of the flame as an indicator of its noise is then extended to a flame-driven Rijke tube. This demonstrates the versatility, transportability and robustness of the techniques developed. The experiment is of practical interest because of the close links between the Rijke tube phenomenon and that of 'reheat buzz'.