山田's voice came falling from behind.
What is the nuance implied by 降る here?
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Putting aside the fact that the sentence 3 is uncommon and a bit literary, the semantic nuance of the sentence 3, if any, is that the voice came unexpectedly and suddenly.
A figurative expression "空から降ってきたような話" means "sudden and unexpected offer". There's an idiomatic phrase 降って湧く which means "(something) happens suddenly and unexpectedly".