ANSWERS: 3
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lol, why would you even want to listen to the radio!
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Assuming you are inside a closed cabin and the radio is with you, certainly. The air between you and the radio is at rest relative to both, so sound travels normally. If you are travelling at the speed of sound in an open cockpit, then you have more problems than listening to the radio, which you could only do if it was in front of you.
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This is incomplete as a question, since it does not make something explicit which is crucial. Suppose you are inside an enclosed cockpit, in a jet that is moving at the speed of sound. The air in that enclosure is also moving with you. So sound, which is merely a set of vibrations in the air that you interpret as a voice or music, will be fully understandable to you as long as you can hear it above any background white noise. Suppose instead, that you are able to ride your bicycle at the speed of sound in air. Now, your ears are unenclosed. A radio on the handlebars is blaring away. This sound will be essentially washed away, unavailable to your ears as sound. Of course, at that velocity, your ears would probably be torn from your head by the wind, and your eardrums would be damaged too. Finally, suppose that the music blaring on the radio is rap music? Since, to my ears, this is already indistinguishable from white noise in any context, no it would never be heard. That part is just my generationally biased opinion though. ;-)
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