The purpose of this paper is to explore excitation of acoustic mode in a Rijke tube via a flame transfer function (FTF). The Rijke tube, a simple but effective model to represent thermoacoustic instabilities, represents the unstable heat release and acoustic fluctuations. The study employs linear stability analysis with the FTF employed to model the dynamics of the heat release response. The outcome indicates that heater power has the greatest effect on the onset of instability, and heater power is linearly related to the growth of instability. The value of the control parameter above which the instability takes place is determined, which indicates the effect of acoustic damping in retarding the onset of instability. The results establish the cause-and-effect of thermoacoustic instability and identify factors for effective design of control mechanisms to eliminate combustion instabilities in actual combustion systems. The research sets the significance of realistic heat release kinetics modelling in achieving effective predictions of the emergence of instability. Experimental verification and adaptive controls need to be explored further to attain stability in actual combustion systems.