https://www.youtube.com/watch?v=j-zczJXSxnw Instructions for this Discussion The

Question

https://www.youtube.com/watch?v=j-zczJXSxnw

Instructions for this Discussion The Tacoma Narrows Suspension Bridge collapsed as a result of 40-mile-per-hour (64 km/h) wind conditions on the morning of November 7, 1940. A video of the collapse can be found here Discuss physics principles that could have led to the collapse. Estimate the period and wavelength of the standing wave. (The full bridge length was around 1800 meters, but the longest span was 850 meters.) How could 40 mph winds cause such damage? How could the collapse have been avoided? Make an initial posting before replying to other threads. Grading Criteria This assignment is worth 6 points. For full credit, engage in a discussion with at least one of your classmates who posted a different response than you, justifying your answer.

Explanation / Answer

The Tacoma Narrows Suspension Bridge was constructed in such a way that it was very flexible. It was not really like a metal rod but like an elastic rubber stretched between two points. Now if you have a string between two fixed points, you can make it go up and down by pulling or pushing it at any point (preferably centre). The string naturally oscillates at a natural frequency which is characteristic of every system. If you have ever pushed your friend on the swing, you would remeber having given the push at the same frequency as that of the swing i.e. if you were giving the push when the swing was at its extreme position near you, you were giving one push per oscillation of the swing. So if the swing frequency was 'n' the frequency of external force was also the same. This leads to resonance. Further, in the case of a string (or the span of the bridge) between two points the wave formed at resonant frequencies are termed standing waves. On November 7, the winds provided the external force to drive the oscillations of the bridge. As this was happening at the resonant frequency, small force was able to produce large effect (just like the swing is easy to push and accelerate in the way mentioned above).

Initially, Frequency was reported as 0.6 Hz and wavelength = 2L/9 = 2(850)/9 = 188.89 m

Time Period = 1/0.6 = 1.67 seconds.

The collapse could be avoided by having holes in girders that would have led to wind passing though them rather than forcing them to osscilate. Having lower span length would also have helped.

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