Humming noise coming from underkitchen sink line. This line is leading to outside of house and drips water frequently. The line is attached to some sort of valve and supplies water to faucet.

Most likely, it is Reverse Osmosis drain tube.

What's a Reverse Osmosis drain tube.

Reverse Osmosis is a filter system usually installed under your sink. It consists of small diameter drip tube that discharges water during filtration process.

Do you have such as system installed? Could you possibly take a photo of your under sink cabinet plumbing and post it for us ? Back to you. Milo