Currently there's a mutex to protect access to finished_source_handlers_ from the main thread and the audio thread.  Since this mutex can happen in the audio thread, there's a potential for blocking the audio thread.

Maybe we can simplify this by removing this mutex and adding a new variable.  The audio thread can update finished_source_handlers_ in the audio thread.  In the post render task, finished_source_handlers can be appended to a new variable.  Since there's a trylock, this new variable won't be updated if the main thread is accessing it.  If the lock succeeds, the copy can proceed and finished_source_handlers_ can be cleared safely.  It's ok to skip the copy since it will get picked up next time around.