Question

9. A microwave oven has a frequency of 2450 Hz. You can use mini-marshmallows to locate the nodes of the standing wave inside the microwave. Describe how to measure the speed of light using mini-marshmallows and a microwave oven.

Answer 1

(1.)The firstly, Measure the distance between two nearest-neighbour “hot spots”. This is your λ/2 value. It might seem a little like cheating, but because you can’t measure it directly without pulling your microwave apart and putting yourself in danger, you need to take advantage of the sticker on the back of the microwave oven that tells you about its operating parameters. Included on this sticker is the microwave frequency your oven uses. As you can see, the microwave oven used for this demonstration uses a frequency of 2450 MHz.

(2).

Suppose, In this demonstration, was found to be 7 ± 1 cm. f was given as 2450 MHz.

Therefore we can calculate:

c = f•λ

= (2450×10^6)×(2×7×10^-2)

= 3.4×10^8 m / s

This is about right, but a little off. There was some uncertainty in my measurement of the half-wavelength, though, which I can now include in my answer. I recorded an uncertainty of 1 cm. I can convert this to a percentage of 7 cm, and then back to an uncertainty value in my final calculated speed.

%Uncertainty    = 1 / 7 = 14%

Uncertainty in c = (0.14×3.4)×10^8 = 0.5 × 10^8 m / s,

meaning my final answer should be expressed as c= (3.4 ± 0.5) × 10^8 m / s