Vibrations and Waves Legacy Problem #3 Guided Solution
Problem*
The spin rate of a CD-ROM varies according to the location on the disc from where data is being accessed. When accessing data from the inner circles of the disc, the CD can spin at a rate as high as 400 revolutions per minute. Determine the frequency (in Hertz) and the period (in seconds) of the spinning CD.
Audio Guided Solution
A common confusion of students is confusing the concept of frequency with the concept of period. They have very similar, yet opposite, definitions and formulas. In the case of frequency, we would define it as the number of things which happen per unit of time. It's the number of happenings, or number of things happening, per second, often expressed in units of hertz, which means per second. The period, on the other hand, is the time period, or the time it takes for the number of things to happen. So in this question, we're talking about a CD, which is spinning, making 400 revolutions, that's the things that are happening, in one minute, which can also be interpreted as 60 seconds. We wish to determine the frequency in hertz, and the period in seconds. To determine the frequency, you have to take these number of things which are happening, and divide by the time. That's 400 revolutions, and you'll have to divide by 60 seconds. This gets the answer in units of hertz. It comes out to be 6.666 repeating. We can round that to three significant digits. In the case of period, we have to do it just the opposite way. We have to take the time and divide by the number of things which are happening. Sixty seconds divided by 400 revolutions gives me the time period, or simply the period. It comes out to be .150 seconds.
Solution
Frequency = 6.67 Hz
Period = 0.150 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.
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