Dear Gabriel Pehlarovich:
If the problem only happens when you add an audio sink block to the code, my guess is the (hardware-level) clock mismatch between the SDR master clock and the master clock used by the audio source (a.k.a. "two-clock problem"). I never used E310, so I am not sure if the clock of its audio i/o has any relationship with the clock of the LO used for the radio transmission, but this is a quite common problem.
Try searching for something like "two clock problem gnuradio" using your favorite search engines, and you will get a lot of relevant archived discussions (..but the fix can be nontrivial).
Regards,
Kyeong su shin