Is it possible to use arduino to capture the music on PC or any other music device (through its 3.5 mm audio output) and transmit it wirelessly to my headphone, I mean to some small wifi device with 3.5 mm jack where I can plug my headphones ?
why not to buy wireless headphones?
In theory you could - but it would likely be monophonic only, and very poor quality (maybe telephone quality?)...
If you've got a set of headphones with a build-in FM radio you could use a FM transmitter such as NS73M
Sparkfun have a board for them