I have had my beats studios sitting on my shelf for quite some time now and they're just collecting dust now. The last time i used them they snapped right where the length extensions are (See Pictures) when i went to place them on my head, Does anyone know what is the best solution as to fixing these? I know this may not be the best place to ask for help on this but i just want to get them working again. I believe they still work fine it is just physical damage.
You would probably lose the ability to adjust them but as long as they are properly adjusted to begin with you could use a couple of layers of auto repair fiberglass cloth and rosin to hold the pieces together. Tightly wrap the pieces at least an inch or more above and below the joint and apply the rosin. You can get the auto repair fiberglass cloth and rosin at auto parts stores and some hardware stores. It won't be pretty but it should work.
Search "auto body repair fiberglass cloth" and you'll find a lot of sources and how-to videos.
drill two holes at either end of the headphones while the pieces are attached. procure 2 small bolts and nuts.
the bolt will go through the outer earpiece, through the center headband and will secure both.
that side will not be adjustable anymore.