Originally, George Lucas had seen a British documentary on PBS about the Battle of Stalingrad in World War II and had noted that the firing sound of some strange Nazi rockets was quite weird and interesting. Lucas mentioned that it might make a great sound for the laser gun and Burtt managed to find a copy of the documentary. He then set about finding sources that could emulate that sound. Luckily, at Twentieth Century Fox Studios, Don Hall let Burtt go through the Fox sound library, where he found recordings of some elephants that had been done for an Errol Flynn movie The Roots of Heaven [1958]. In that film, elephants stampeded and bellowed. with an almost shrieking sound (the same sounds were used for the dinosaurs in Journey to the Center of the Earth).
After making a copy of that recording, Burtt realized that when he slowed it down and stretched it out, he ended up with a sound similar to the rocket one in the PBS documentary.
But it wasn't quite right, so Burtt took the sound of the elephant and mixed it with pass-bys he'd recorded of cars during a rainstorm as they sped through puddles in front of a motel where he was staying (a pass-by is when a vehicle comes toward the viewer, passes by, and then speeds away).
[etc]