In other words, what is the similarity between a lightning bolt and a wobbling sheet that make them sound alike?
It seems to me that the two systems have a much different way of moving the air, and probably if you could hear it up close, a lightning bolt wouldn't make the sound of a wobbly metal sheet. I think maybe the many reflections and how they interact with the cylindrical shape of the thunder-wavefront may be what gives the similarity.
Best Answer
Here is a thought:
With some experimentation, I've found that a sheet, when wobbled gently, makes a 'wub' sound which has a different spectrum than rolling thunder. However, when wobbled violently, the sheet forms bulges which narrow and sharpen and then suddenly flatten, making a loud 'blap' like a thunderclap. The reverberations in the sheet of this flattening seem to give the rolling effect of thunder.
Indeed, the sudden flattening looks like it creates a the sort of sharply single-peaked pressure wave I expect close to a lightning bolt. I asked a friend who lives where there is plenty of lightning, and he confirmed that close to lightning, there is no rolling thunder.
This suggests to me that there is a similarity between how the flattening reverberates in the sheet and how the thunderclap reverberates across a landscape.
EDIT: I don't think the sound comes from the whipping effect at the bottom of the sheet because a similar sound happens with an aluminum foil sheet, where the sound is definitely not coming from the whipping of the bottom, which doesn't get very fast with aluminum foil.