Burning carbon-free fuels such as hydrogen in gas turbines promises power generation with strongly reduced greenhouse gas emissions. A two-stage combustor architecture with a propagation-stabilized flame in the first stage and an autoignition-stabilized flame in the second stage allows for efficient combustion of hydrogen fuels. However, interactions between the autoignition-stabilized flame and the acoustic field of the combustor may result in self-sustained oscillations of the flame front position and heat release rate, which severely affect the stable operation of the combustor. We study one such ‘intrinsic’ mode of interaction wherein acoustic waves generated by the unsteady flame front travel upstream and modulate the incoming mixture resulting in flame front oscillations. In particular, we study the response of an autoignition-stabilized flame to upstream traveling acoustic disturbances in a simplified one-dimensional configuration. We first present a numerical framework to calculate the response of autoignition-stabilized flames to acoustic and entropy disturbances in a one-dimensional combustor. The flame response is computed by solving the energy and species mass balance equations, coupled with detailed chemistry. We validate the framework with compressible direct numerical simulations. Lastly, we present results for the flame response to upstream traveling acoustic perturbations. The results show that autoignition-stabilized flames are highly sensitive to acoustic temperature fluctuations and exhibit a characteristic frequency-dependent response. Acoustic pressure and velocity fluctuations can either constructively or destructively superpose with temperature fluctuations, depending on the mean pressure and relative phase between the fluctuations. The findings of the present work are essential for understanding and modeling the intrinsic feedback mechanism in combustors with autoignition-stabilized flames.