But it still takes time for the sound to reach you. And in that time the source has continued to move. So it will be as if you are watching a video but hearing with a tape delay.
If some one was standing 1000 meters away from you, and had a sign that flashed a sequence of numbers, 1,2,3,4,… once per second, and at the same time as the number flashed, they shouted the number loud enough that you could hear it, do you think what you heard and what you saw would be in sync?