Consider a rope hanging from the ceiling, length L and mass m, which is free at the bottom. It is excited at the top sinusoidally, so that a traveling wave is moving downwards. The amplitude of excitation is smallest at the top and increases towards the bottom. Estimate the dependence of the amplitude on z, the distance from the top.

Hint: Use the conservation of power - the power of the traveling wave at the top remains constant throughout the length of the rope.

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