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Wednesday, February 22, 2012

Measure the Speed of Light with Chocolate

"'C' is for chocolate! 'c' is also the symbol used for the speed of light. Defined as being 299,792,458 meters per second in vacuum, you can take a crack at measuring the ultimate speed using your microwave, a ruler and a bar of chocolate! Yum!" (Jefferson Lab - YouTube)
Well, lets see how they do it:




And now the calculations:


To calculate the speed of light, we can use the math's expression of speed:
v = Dx/Dt
In this case, Dx = l and Dt = T and T = 1/f (T is the period and f the frequency of the wave, and the wavelength).
The holes that appear in the chocolate corresponds to the maximum and minimum in a steady wave. So the wavelength is two times this distance:
l = 2 x 7.1 cm = 2 x 7.1 x 10-2 m
The frequency can be read in the back of your microwave. In this case, the value corresponds to f = 2 450 MHz = 2 450 x 106 s-1.


So, velocity is:
v = l x f <=> v= 2x(7.1 x 10-2 m) x (2 450 x 106 s-1) = 3.48 x  108 m s-1 .


That brings a percent error:


e = |c - v|/|c| x 100 = | 2.99 x  108 - 3.48 x  108|/|2.99 x  108| x 100 = 16 %
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