Why did the radio tower collapse in the middle if stable at top and bottom?

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pooka
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A certain radio tower was stabilized at the top with guy wires, and at the
bottom with a concrete foundation. So, it was stable at the bottom and at the
top. In windstorms, it wobbled violently in the middle. Eventually the tower
collapsed. Using wave theory, explain why this happened and offer suggestions
about what could have been done to prevent it.

is the wave theory, the particle duality one? if so, i still don't understand why the situation described is related.
 
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Its just asking you to use your knowledge of oscillations and waves to describe how the tower could have collapsed.
 
Borek said:
Think in terms of nodes positions.

Hmm...would this be a standing wave then? I'm still a little confused, because in the middle, isn't it the node, which is a point of no displacement? The antinodes are at the top and bottom and should undergo the maximum displacement during each vibrational cycle of the standing wave. So why would the middle collapse?
 
Why do you think the fixed ends would be antinodes?
 
Could be, could be not. Depends on the wave number.
 
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