Vibrations and Waves Legacy Problem #2 Guided Solution
Problem*
Strong winds can apply a significant enough force to tall skyscrapers to set them into a back-and-forth motion. The amplitudes of these motions are greater at the higher floors and barely observable for the lower floors. It is said that one can even observe the vibrational motion of the Sears Tower in Chicago on a windy day. As the Sears Tower vibrates back and forth, it makes about 8.6 vibrations in 60 seconds. Determine the frequency and the period of vibration of the Sears Tower.
Audio Guided Solution
A common complaint which I often hear from students is I just can't figure out what formula to use. And oftentimes figuring out the formula is a matter of figuring out the concept. If you know the concept, the formula follows. And here in this question, the concept has to do with the distinction between the frequency and the period. So what you ought to know is that the frequency is the number of things which happen per unit of time. And the period is just the opposite. It's the time it takes for the number of things to happen. And in this problem, the object that's moving or vibrating is the Sears Tower, vibrating back and forth and making 8.6 vibrations in 60 seconds. So if we wish to determine the frequency, we need to divide the vibrations by the seconds. It ends up being 8.6 vibrations divided by 60 seconds, and it comes out to be 0.1433 vibrations per second, also known as a hertz. We can round this to two significant digits. Now if we wish to find the period, we have to do it just the opposite way. We have to do the seconds divided by the number of vibrations. The 60 seconds divided by 8.6 vibrations gives 6.9767, which I can round to two significant digits.
Solution
Frequency: 0.14 Hz
Period: 7.0 s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = 12.8 \unit{\meter\per\second}\), \(\descriptive{λ}{λ,wave length} = 4.52 \unit{m}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
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