i think the noise is originating from the faucet and not the drain.

doesn't the vanity share a common discharge pipe?

If your using the hot water side of the faucet as the hot water moves through the piping it expands and this could very easily cause sounds of expansion and contraction.

vents have air thus no "poping" will be heard Also like Larry said it could be a faucet lose washer causing sounds

Thanks to both of you for the replies. I originally thought it was the hot water line too and that the pipe was expanding/contracting until I started trying different combinations throughout the bathroom to narrow it down. It also does it the cold water running, though. My hot water heater is in the attic maybe 25 feet from the sink, but my supply line runs down the outer wall of the house to the crawlspace and back up to the other floors (seems wasteful to me). We theorized the vent problem since I hear the noise overhead. Could a fixture problem sound like it's overhead with the mirror acting like a sound dampener? Just another theory...

it only does it on the one side?

try removing the aerator from the tip of the faucet and flush the lines out for a couple minutes and see if anything changes.

PVC has a high Coefficient Of Expansion..

Sometimes you'll get a "ticking" noise as the expanding PVC/DWV lines past thru framing members that are too tight/too small holes or restricted in length....

Does the noise follow the use of HOT water down the drain ?

....as a Test DON'T use the bath faucet.... use a bucket of hot water from the kitchen......Noise ?

Outside cold wall ?

What is the supply line pipe ?

"......measure Once.....cut Twice....

throw that one away and cut a new one...."

You are correct. The vent pipe, or "stack" is likely the cause of your frustration and Doug Seibert nailed it. I'm betting that when it's very cold outside and you run hot water the noise is louder. I pulled off the baseboard behind my toilet and found the stack to be located in the wall about 16" from the back of the toilet towards the sink using a drywall saw. The sole plate (2"x4" board that runs along the floor) was in contact with the stack pipe. I used a sawzall (carefully - at an angle to avoid cutting the stack) and removed the piece (a "cat's paw" works well to pop out the piece(s)). See picture. I just covered the area with some beadboard behing the toilet. Should've done this years ago - 10 minutes of work. See photo.