Previous theories modelling unsteady one-dimensional flames are extended so that the effect of upstream and downstream noise interference is included. Using the fact that the Mach number M is a small number, the principles of matched asymptotic expansions are used to link long wavelength acoustic disturbances at large distances [0(\f~l) on a diffusion length scale] from an anchored flame to small perturbations in velocity within the combustion zone. This matching process yields a frequency condition governing the flame vibration and a number of cases are illustrated in the paper.