You may not have any problem other than the float bowls being dry. A lean air / fuel mixture can cause an engine to back fire through the intake. (A rich mixture will be through the exhaust.) With the float bowl being dry, the mixture is likely to be lean while the float bowl is filling.

If it was my car, I would very carefully check out the ignition system to make certain there is not an ignition problem as well. It is entirely possible the car has two problems. Gasoline burning inside the carburetor is not good!!