This stems from a riddle I read in a magazine perhaps 20 years ago so I apologise for the imprecise recollection.
A dog that can run infinitely fast is placed on an infinitely large flat surface and an alarm clock is tied to his tail. The dog has been trained to double the speed he is running when he hears the bell go off.
So this dogs sets out running at, let's say 5 m/s and every 10 seconds, the alarm goes off. The question is how fast is he running after two minutes.
Also can someone find the actual riddle? I have not been able to.
I have cloaked the rest of the question in case you want to answer that one first.
So the tricky part of this is of course that the dog supposedly stops doubling his speed after he doubles past the speed of sound, outrunning the alarm My question is, would he not intercept previous sound waves and start doubling again?