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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?

Thanks

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What happens is you overtake one of these previous sound-waves? The frequencies will be shifted up, so at some point the dog can't hear those anymore at some point? – Bernhard Jan 27 '12 at 14:38
And they would be fainter as well. – queueoverflow Jan 27 '12 at 17:02
The sound waves will travel through his body so he will always hear the alarm very quickly. – Philip Gibbs Jan 27 '12 at 19:06
Assume the alarm is on a string that does not carry the sound – mplungjan Jan 27 '12 at 19:13

1 Answer

up vote 4 down vote accepted

There are only a non-infinite number of waves that escaped the dog. So he will double a couple more times, and then he will reach his final speed.

I wrote a small Python simulation for this. The output of the program is also on the same gist page.

To run it, download dog.py and call it with python dog.py, assuming you have a python interpreter on your machine.

It starts off with 6 waves catching the dog, and then the dogs catching the waves.

So I think there indeed is one final speed, the program suggests 20480 m/s. This is only true, if the dog can hear the faint and differently pitched sounds.

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Yes, that would be my thought, but that would be faster than the riddle-writer expected as answer in my opinion Can whoever voted this down tell us why? – mplungjan Jan 27 '12 at 15:04
The Python program looks cool. Can you run it on github, or do you have to download it, compile and run? Could you just post the output yourself? I mean, you went through all the effort to write that after all. – AlanSE Jan 27 '12 at 18:13
You have to download the file and call it with python dog.py, assuming you have a python interpreter on your computer. – queueoverflow Jan 27 '12 at 18:30
@mplungjan The original post didn't include the Python script. So now it is improved. Adding figures would improve the post even further. – Bernhard Jan 27 '12 at 18:32
That was fun :) – mplungjan Jan 27 '12 at 19:16
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