Two problems:
1: Use an NPN instead of a PNP - or better yet, an N-channel MOSFET. Essentially you're making a low-side switch.
2: Most importantly: this is never going to work with just one wire between the MP3 player and the Arduino. Your setup will work in essence (I'd use an N-MOS), but you'll have to connect the MP3 player's GND to the Arduino GND.
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