What causes the pressure to build during a deflagration if the reaction front is moving slower than the pressure wave?

Answer

The gases are expanding faster than the flame front can consume the unreacted material

In a subsonic deflagration, the pressure increases because the rate of gas expansion driven by combustion outpaces the rate at which the chemical reaction consumes the fuel.

What causes the pressure to build during a deflagration if the reaction front is moving slower than the pressure wave?
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