Thursday, July 31, 2008

Answer: Writhing Chain
New Problem: Hourglass

Writhing Chain
The speed of sound in the chain depends on its tension, the same way it does in a violin string. You can raise the pitch of a violin string by tightening it. Similarly, the speed of traveling waves increases where the chain has increasing tension. The tension in the chain is high near the top because it's supporting the weight of all the chain below it. Near the bottom, the speed is low. The chain is set to rotate at just the speed of traveling waves near the bottom of the chain. That way, patterns can persist there even as the chain cycles around.

You sit an hourglass on a scale with the sand in the top, but blocked from falling. Then you remove the block and let the sand fall down the hourglass. Make a plot of the reading on the scale as a function of time.

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