This is purely an exercise in “What if?” Automobiles, of course, aren’t built sleek enough or strong enough to exceed the speed of sound or to withstand the physical stresses of the sound barrier. But it’s fun to think about. The answer is simple: Yes.
Or, I could have posed a different question that would settle the issue: On the supersonic Concorde airliner, can the passengers converse? At those prices they’d better be able to. But how, if they are traveling faster than sound?
Even if you were driving faster than the speed of sound, you and the car and the radio and your terrified passengers would all be moving at exactly the same speed relative to the countryside. You’re all in the same boat, so to speak.
As far as sound is concerned, the important thing to realize is that you and the radio and the air in between aren’t moving relative to one another. The radio has the same spatial relationship to you as if the car were standing still. It emits its sound waves through the car’s air to your ears with the speed of sound as if nothing unusual were happening, because inside the car, nothing is. In fact, if the speedometer and windows were blacked out (God help you), you wouldn’t even know you were moving except for the noise and vibration from the wind and the tires.
What if you were driving a supersonic convertible with no windshield and the radio speaker in the back? Could you still hear it? No. Not even considering the effects of the wind on your poor, battered ears and brain, you wouldn’t be able to hear the radio. The sound waves from the speaker are being transmitted through the air toward you at the speed of sound, but the air itself, the transmission medium for the sound, is moving backward away from you even faster. So the sound will never reach you. The sound is like a rowboat rowing upstream more slowly than the water is flowing downstream.
By the way, the radio receives its signals by radio waves, not sound waves, and radio waves travel at the speed of light, which is a million times faster than the speed of sound. So any motion of your car is certainly not going to have any effect on the radio’s ability to play.
Now what about the sounds that escape from your car? What would a roadside cow hear? (You’re not doing this on city streets, I hope.)
Your car noises, whether from radio, tires, engine or screaming passengers, are being sent out in all directions at the speed of sound. But you are approaching the cow faster than that; you are actually outrunning your own sound. As your car approaches the cow, then, she can hear none of the car noises that are trailing behind you until shortly after you pass, when she will hear a sonic boom and all the car noise.
Note that if you are outrunning sound, you won’t be able to hear any sounds coming from behind you, because they can’t catch up with you. That’s why you can see the flashing lights on that police car that’s chasing you, but you can’t hear the siren. I doubt, however, that the trooper will accept that as an excuse.