The interaction of a shock wave with an existing fast flame (convection-reaction driven) is considered whereby the driving piston is not at a constant speed. Between the shock and the flame, there is an induction zone which governs the acoustic coupling between the flame and the shock. The asymptotic matching of this zone to the regions near the flame is presented. The case of a variable piston speed is allowed so that pulsed transient inputs to fast deflagrations can be simulated.