Simulate sound cheerfully (4)

I believe the answer is:

fain

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'cheerfully' is the definition.
Both the answer and definition are adverbs. Maybe you can see a link between them that I don't see?

'simulate sound' is the wordplay.
'simulate' becomes 'feign' (synonyms).
'sound' shows a homophone (sound like).
'feign' sounds like 'FAIN'.

Can you help me to learn more?

(Other definitions for fain that I've seen before include "Willingly (archaic)" , "Glad" , "Gladly" , "willingly behind the times" .)

I've seen this clue in The Globe and Mail.

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