From observations from my actual job which gets very tedious with quotas so I have to track my numbers and make sure I'm meeting company demands, music does slow me down but keeps me sane.
That said, white noise is the best of both worlds. I produce faster than with music and the silence and tediousness doesn't kill me while I work. Whatever works bets for you though. You can probably test it out by timing how many Sudoku puzzles you can complete in a given time frame using one of those free random generating apps. See what's better for you, music, no music, or white noise.