## Help!

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### Help!

I am doing the science fair project "Measuring the speed of light with a microwave oven." This is a project available on the ScienceBuddies website. I don't know how to use the edge measurements to get an upper and lower bound for my measurement. All it says is ".Measuring the "center-to-center" distance between adjacent cooked portions will give you the average spacing of the hot spots. Measuring the "edge-to-edge" distances (both shortest and longest) between adjacent cooked portions will give you upper and lower bounds on the error of your measurement" Any advice?
Braylie

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Project Question: I am conducting the experiment "Measuring the speed of light with a microwave oven" I am confused about how to go about creating an upper and lower bound on the error of measurement. It says to "Measure the 'edge-to-edge' distance (both shortest and longest) between adjacent cooked portions ill give you upper and lower bounds on the error of your measurement." If anyone can tell me how to go about this and give me the math, please do.
Project Due Date: 02/6/13
Project Status: I am finished with my experiment and analyzing the data

### Re: Help!

Hi Braylie,

I looked at the project page; the shortest edge-to-edge distance will give you a lower bound, whereas the longest edge-to-edge distance will give the upper bound, just as the procedure states. As you probably already know, the error in this experiment comes from estimation of the locations of the "correct" edges and centers, as well as from the spacing of markings on the ruler. I'm not sure if this was much help in terms of clarification, but stay tuned for other experts' takes on your question!
Need an idea or some inspiration?
http://www.sciencebuddies.org/science-fair-projects/project_ideas.shtml

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Enjoy!
-RM, Expert
Goldenzenith
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### Re: Help!

Hello,

The upper bound error measurements mean the difference between the two extreme edges of the hotspot i.e. the leftmost edge of one hotspot to the rightmost edge of the other hotspot. The lower bound error measurements mean the difference between the two nearest edges of the hotspots i.e. the inner left edge of one hotspot to the inner right edge of the other hotspot.

Note that since there is no observable center of the hotspots, there is an intrinsic error in whatever value for the speed of light you get from the center-to-center measurements since there will be many "correct" center-to-center measurement. This is where the upper-bound and lower-bound measurements come in to give you an idea of the error. These two numbers form your confidence-interval and your margin of error.

Confidence Interval = (Upper Bound Measurement - Lower Bound Measurement)
Margin of Error = 0.5 * Confidence Interval

This means that you only have confidence if the center-to-center measurement is less than the upper-bound measurements and more than the lower-bound measurement and there might be an error within the margin defined above. The error carries forward in all calculations you do with the point number i.e. the center-to-center measurement. So you will have to find the error in the final speed of light of the microwaves using your margin of error in your calculations for the speed of light.

One way to present your data would be to say something like (Final Speed from Center-to-Center Measurements) plus/minus (Final Margin of Error on Speed of Light).
Ex. Speed of Light = 3*10^8 m/s [&plusmn] 0.5*10^8 m/s.

I would suggest that you look up Point Estimates, Confidence Intervals and Margin of Errors and you will have a better understanding of this.

Hope this helps and if you still have questions, let me know.
Dharman Kothari
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DharmanKothari
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### Re: Help!

The [&plusmn] is supposed to be the plus or minus sign. Let me know if you have questions.
Dharman Kothari
Volunteer Expert
Science Buddies
DharmanKothari
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