RGB LED strip, powered by an ATX PSU and controlled by PWM, makes my speakers buzz with Arduino connected by USB
It sounds like your audio cables are carrying the PWM frequency to the monitor/speakers. This could be confirmed if you speed up or slow down the pwm frequency in the arduino and see if the "tone" you hear coming from the speakers gets lower or higher in pitch.

You mention that the audio cable carries your projects GND? I don't quite understand what you mean but if you mean your project shares a common ground with your audio signal that could definitely be the disturbance. 

Start by trying to power the arduino through different USB ports. If that doesn't fix it, try and power the Arduino with something else like a phone charger so that your LED project is completely isolated from the computer.