The trumpet has no reeds. It is a brass instrument, which means
the mouthpiece is a single piece of brass.
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no, it has a mouthpiece where you "buzz" your lips.
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That's correct.
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No, trumpets are brass not woodwind. The only instrument that
looks like brass but is woodwind is the saxaphone, a single reed
instrument. Trumpets use a mouthpiece with no reed.