We've all had it happen - your favorite headphones become useless due to the helpful attentions of your pet. (In this case, my young tabby tomcat Mr. Toes!)
Step 1: Taking Them Apart
Take apart the side of your headphones that the broken cord connects to. The ear pad pops right off, and the speaker is held in with three (3) small screws. Remove all three (3) screws.
Step 2: Look at the Wires
The incoming cord has three (3) wires - green, blue, and copper.
Step 3: Look at Where the Wires Connect
The blue wire is connected to the blue and red wires that go up through the headband.
The green and copper wires are connected to the speaker AND to the matching wires going up through the headband.
Step 4: Additional Wiring
I also took a look at how the right side was wired, since there was an existing headphone jack for sharing your sound with a friend.
On this side, the blue wire and the copper wire from the headband are connected to the speaker, with the copper wire then continuing on to the headphone jack. This also gave me an idea as to the size and type of headphone jack I needed.
Step 5: Cut the Cord Off
Next, cut the damaged cord off, giving yourself several inches to work with. Then untie the knot that holds the cord in place, and remove the cord and the rubber cord protector.
Step 6: Assemble Materials!
Next, you need to aquire a small headphone jack that will fit in the existing cord hole, a pencil soldering iron, and some good solder.
(It also doesn't hurt to watch a few videos on how to solder, for those of us who don't do this much)
I cannabalized an old ipod dock for my headphone jack.
Step 7: Solder the Wires
Next, solder the green, blue, and copper wires onto your new headphone jack.
Step 8: Reassemble Your Headphones and Test!
Reassemble your headphones and test your new headphone jack using a simple male-to-male audio cable.
And now, having done this, you can also note that it does not matter which of the 2 headphone jacks you use - they both work the same.