There is a traditional rain stick (percussion instrument) in Africa, Latin America, and I believe in Australia as well. Was it invented separately, or did one culture influence another?
Here is a demonstration of the sound of a rain stick:
It is my understanding that civilization originated in Africa and human migration patterns have moved from continent to continent around the globe from that point. If the rain stick was developed before human migration started then it's possible it was carried from one place to the next. But the idea is a rather simple idea and there is no reason several people might not have the same idea in the different cultures that have developed over time, so I think you've managed to ask a question where it's conceivable no factual answer really exists.
The rain stick is a variation on the rattle, which has been invented by every primitive culture (and continues to be invented by every toddler).
Even without documented examples of ten thousand year old rainsticks on separate continents, independent reinvention is plausible enough for a concept as simple as this.