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How is this question ambiguous?

Who knows when the train will arrive?

The sentence is ambiguous and I have to argue the reason of its ambiguity focusing on the interpretation of the wh-adverb. And what would the syntactic trees for both interpretations look like?

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    I can suggest such kind of ambiguity: that question can be either concrete or rhetoric, which changes its meaning: in the first case we really want to find out which person knows the information about the train, in the second case we regret that it's not known when the train arrives and/or whether it will arrive at all.
    – Yellow Sky
    Apr 6 at 14:08
  • "Who" is not an adverb but a noun phrase. "when the train will arrive" is a subordinate interrogative clause, where the meaning is "Who knows the answer to the question 'When will the train arrive?'" The ambiguity that Yellow Sky refers to is still there.
    – BillJ
    Apr 8 at 7:17
  • @BillJ - In fact, there is a wh-adverb there, it's ‘when’, and it can be a source of another kind of ambiguity since it can be either interrogative or relative. In the former case it's as it is, a question about a person who knows the information about the arrival of the train, but in the latter case it's pretty weird, suggesting that there's an imaginary world in which at the time of the arrival of the train some people do possess knowledge (i.e. ‘know’) and some don't, so the question looks like asking, “At those times when the train will arrive, who possesses knowledge, who knows?” :)
    – Yellow Sky
    Apr 8 at 14:20
  • @YellowSky Yes, there's no doubt about the ambiguity, as you say. Incidentally, I follow Huddleston by classifying "when" as a prep -- But that's another story!
    – BillJ
    Apr 8 at 15:52

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