If a pilot flies his plane faster than the sound, does he still hear any sound in his cockpit? If so, how come, he basically leaves all sound behind him?

Answer

If an aircraft is going faster than the sound, sound produced behind it cannot overtake the pilot. Sound produced by, for example, the turbulence of the exhaust (an important source of noise after all) can no longer reach the pilot. But noise produced in front of or in the aircraft (turbulences at the nose, vibrations in the structure of the aircraft) can still be heard.