When the hot water faucet is turned on the pipes in the basement vibrate, cause and solutions please.

Any hot water faucet or just one?

Just one at this time.

I'm surprised Tom hasn't been back here today to further explain what's going on. I suspect that your hot water faucet has a loose washer that is fluttering when you open the faucet. Shut off your main line and open the faucet stem, inspect for debris and /or loose washer.