I bought a new kitchen faucet 2 years ago with one handle to control the hot and cold water. The sound just started occurring this past year, it happens when I turn the handle towards the hot water only.

The house I live in is approx. 40 years old with copper piping supplying hot & cold water throughout the house.

It sounds like you have a loose washer inside the angle valve,Turn on the hot water go under the sink and turn the angle valve all the way in and out see if the noise stops, if it does then you have a loose washer, you will need to remove the stem and replace the washer see the image below, good luck

I have the same problem. It's the valve inside the faucet that diverts water to the sprayer when you press the sprayer. It's very easy to get to from the top of the sink without unscrewing any pipes or hoses, but make sure the water is off. Unfortuately, the valve seems to be completely sealed and there is no way to get inside it to replace the faulty piece that vibrates and makes the noise. You can ,however, request a new valve from American Standard since the faucet has a lifetime warranty. It's very easy to install yourself.