This paper explores some fundamental issues involved in flame-acoustic interaction in the context of non-premixed flames. The combustion model considered is a two-dimensional co-flowing non-premixed flame in a uniform flow field, as in the Burke-Schumann geometry. Both finite-rate and infinite-rate chemistry effects are examined. First, the velocity-coupled response of the flame to an externally imposed velocity fluctuation is studied at various frequencies of interest. The Damköhler number plays an important role in determining the amplitude and phase of the heat release fluctuations with respect to the velocity fluctuations. Second, the combustion model is coupled with the duct acoustics. The one-dimensional acoustic field is simulated in the time domain using the Galerkin method, taking the fluctuating heat release from the combustion zone as a compact acoustic source. The combustion oscillations are shown to cause exchange of acoustic energy between the different natural modes of the duct over several cycles of the acoustic oscillations.