Is this on a laptop or PC? If it is, check the sound device in device manager and see if there are any errors. You can also try updating the driver. If the problem is the jack itself, the easiest fix is to pick up a USB sound adapter.
If the problem is the "plug" on the headphone cable then it may be replaceable. https/www.amazon.com/Repair-headphone-earphone-headset-Soldering/dp/B00JDE8FTC
It will need to be soldered on the headphone cable. There should be someone in the college audio video or tech support that can do this for you. They likely have the plug too. Be aware that some headphone cables are not meant to be soldered to and resist repair.
If the problem is the "jack" which is on whatever you are plugging the headphones into that is more involved.