The most common and most likely answer to this crossword clue is the 8 letter word TINNIEST
I've seen this crossword clue in The Guardian
T
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N
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T
Buddy explains!

The straight part
We know that "Like sound from worst headphones" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like sound from worst headphones = tinniest.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TINNIEST mean?
TINNIEST adjective- Of or pertaining to or resembling tin.
- Pertaining to the thinness and cheapness of tin or similar-looking metals, in contrast to a heavier, more valuable metal.
- Pertaining to a thin, unpleasant sound recalling that of tin being rapped.