Theoreticly - yes. However, it is impossible to travel
faster than the speed of light. Nevertheless, lots
of cool things happen as you get close to it - you
see the things behind you in a higher spectrum and
the things in front of you in a lower spectrum.
If you are in a plane traveling faster than the speed of sound, you can still hear perfectly fine. And if the noise of the plane were not too loud, you'd be able to hear things outside the plane perfectly fine as well (just with a nice big doppler shift). You just wouldn't be able to hear anything behind you.
Since it is impossible to travel faster than the speed of light, there is no meaning to try to hypothesize what is going to happen when you travel faster than light, so, no, there is not even a theoretical phenomena.