There was a noise coming from the pipe near the washer/dryer connections so I placed a sock in the opening and

Question

now the faucet is slightly dripping and the sock is also wet. I live in apartments, so I'm wondering if this could turn into a serious problem? Would it just be better to remove the sock and deal with the noise?

Answer 1

I believe you are talking about the drain pipe for the washer.  The drain could be partially clogged causing a backup into your apartment which is why the sock is getting wet.  Or by plugging it you are drawing water from the drain as other apartment's washers are draining.  I would definitely contact the maintenance people about the dripping faucet - a very simple fix and you can ask them about the noise.  The noise is probably just other people doing their laundry and you hear the water draining past your apartment.

Answer 2

What kind of noise?  Was the noise only apparent when you use the water, or when you turn off the water?  This may be water hammer.

A water leak is serious, tell your landlord ASAP or a lot of rot and mold could result.