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you have one of 2 problems either
1) the washer in the faucet ( on the stem ) is loose and needs replacement
2) the washer on the valve under the sink has a loose washer and should be replaced
the problem is the washer is lose and as the water passses the washer it opens and shuts the water at a rapid speed it almost sounds like a machine gun
check or replace both and you should be fine
please note first shut off both valves under the sink all the way tight then open all the way 75% of the times this solves the problem