Vibrations and Waves Legacy Problem #4 Guided Solution
Problem*
Like all planets, the planet Venus orbits the Sun in periodic motion and simultaneously spins about its axis. Just as on Earth, the time to make one complete orbit (i.e., the period of orbit) is what defines a year. And the time to make one complete revolution about its axis (i.e., the period of rotation) is what defines a day. The period of orbit for the Earth is 365.25 days, and the period of rotation is 24 hours (1.00 day). But when these same values for Venus are expressed relative to Earth, it is found that Venus has a period of orbit of 225 days and a period of rotation of 243 days. So, for Venus inhabitants, a day would last longer than a year! Determine the frequency of orbit and the frequency of rotation (in Hertz) on Venus.
Audio Guided Solution
In this problem, we're given the period of orbit of the planet Venus and the period of rotation upon its axis of the same planet, Venus, and we're asked to calculate the frequencies at which it orbits and the frequency at which it rotates about on its axis. We understand that frequency is simply the reciprocal of the period. So you'd at first glance think that all you have to do is take the 243 days and the 225 days and take the reciprocal of these numbers. That would indeed give you the frequency, however, it would give it to you on a per day basis. And this question asks us to find the frequencies in units of hertz. A hertz is the number of things which happen per second. So to solve this problem correctly, we have to take the 243 days and the 225 days and first convert that to seconds. Then we can take the reciprocal and that will give us the frequency in hertz. So to go from days to seconds, we need to understand that there's 24 hours per one day and we need to understand there's 60 minutes per one hour and 60 seconds per one minute. So if we take the 243 and the 225 separately and we multiply by 24 and then by 60 twice, that will give us the period in units of seconds. When done for the orbit of Venus, we get 2.09952 times 10 to the 7th and taking the reciprocal of this number gives us about 4.76 times 10 to the negative 8th hertz as our frequency. Doing the same thing for the period of rotation about the axes, we end up with a time period of 1.944 times 10 to the 7th and taking the reciprocal gives us about 5.114 times 10 to the negative 8th.
Solution
Frequency of orbit: 5.14 x 10-8 Hz
Frequency of rotation: 4.76 x 10-8 Hz
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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