Assuming that the dog never tires and can reach any speed
and the metal doesn't fall off:
He will reach 512 m/s at which point he will stop hearing the sound altogether (speed of sound in air = approx. 340 m/s and can differ depending on the air itself but
never reaches 500 m/s) and just keep going with that same speed.
Unless the sound that is transferred via
asphalt (which is almost inaudible but it's there) is enough to keep the poor dog running faster and faster. Then the next speed in this "double the number" progression that is
above the speed of sound in asphalt, which Google flat-out refused to give me just now.
And that "sound velocity in common solids" table I just found? Asphalt
not a common solid?! Jerks.
P.S. I think you changed this one up, unless there's another version I'm not aware of. The original, IIRC, was "how fast does the dog need to go to stop hearing the sound?" to which some people immediately reply "with supersonic speed" while in fact the dog just needs to stop.

You inversed it and enforced the "supersonic speed" thing while wording it in such a way that people forget about it. Nice job!
