My toilet is 6 months old
After I flush my toilet,about 3 or 4 seconds later it sounds like a vibration noise in my pipes in the basement
This has done this for a long time

Hey Ron try this!
I'm assuming that you have a floatball ballcock,(see image). Shut the water off at the stop and remove the three screws on top of the ballcock. Pull the float ball and stem assembly up and out. Pry the washer out and reverse it, being sure to seat it in firmly. Now hold your hand over the open ball cock and turn the water back on for a few seconds to flush out the supply. Reassemble and give it a flush. Sound all gone? Good luck, Tom