The unsteady internal structure of a one-dimensional laminar premixed flame in a one-dimensional harmonic acoustic pressure field traveling normal to the flame is numerically resolved. A two-step competing reaction mechanism with finite kinetics is assumed to occur in the flame in order to examine the role of acoustic transport of the intermediate species on the flame propagation. The amplitude of the incident pressure wave from the cold reactant side is considered to undergo a temperature-dependent decrease when it passes through the flame zone, as the temperature increases due to chemical heat release. The fluctuation in the flame speed, the heat release fluctuation, and the corresponding jump in the velocity fluctuation in the hot product side of the flame relative to that in the cold reactant side are deduced from the solution. The variations of the acoustic impedance and a response function relating the heat release fluctuation to the acoustic velocity fluctuation are reported. It is found that the temperature dependence of the incident acoustic pressure amplitude results in a higher increase in the velocity fluctuation amplitude for a given heat release fluctuation than if the acoustic pressure amplitude were to be assumed constant across the flame. The effect of the heats of the reactions and their reaction kinetics on the above acoustic quantities is parametrically studied. The crucial role of the intermediate species in determining the oscillatory heat release rate is revealed. The results can be used in flame models as part of stability predictions in combustors with pulsations.