which of the below given two sentences is correct? If both are correct, what is the difference in meaning between them?
1)She was heard to sing a song by them.
2)She was heard singing a song
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Both sentences are grammatically correct, although the first one is somewhat unclear: it's in the passive voice, which can lead to having to guess the correct meaning. In this case we're left wondering: Is the song "by them" (meaning, did they write it?) or is the song "heard by them?" If the sentence said, "a song by the Beatles," it would be easier to guess, because the Beatles probably aren't listening.
Finding a better construction in the passive voice would be difficult though: "She was heard by them to sing a song" is awkward and stilted. The second example is better, but doesn't really convey the same meaning. The best and clearest sentence would be in the active voice with no infinitive or gerund:"They heard her sing a song."
I think the real confusion here is about the term "infinitive." Infinitives come in 5 different forms, and here you have another construction entirely. Although "to sing" is an infinitive, you've strayed into the "accusative-infinitive", which occurs with verbs of perception (seeing, hearing) as well as wishing and saying. It's also complicated by the fact that the verb 'hear' (and also the verbs 'see' and 'make') uses a "bare infinitive" (sing) in the active voice, and a "full infinitive" (to sing) in the passive voice.
There's nothing wrong with the passive voice, but as you can see it should be used with caution, and avoided when clarity becomes an issue. Also, using "by" can be difficult, so it's good to learn how to use it properly.
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