In your senior science studies, you may have learned about Hertz and his experiments with what we now recognise as radio waves. Through a series of experiments, he was able to demonstrate that the mystery radiation he was creating with the sparks from an induction coil behaved not only as a wave, by demonstrating that it showed the wave behaviours of reflection, diffraction, refraction and interference, but also that it was a transverse wave, demonstrated by the fact it could be polarised, just like Maxwell’s predicted electromagnetic radiation.
Many of Hertz’s experiments relied on his being able to use the reflection and interference properties of the mystery waves to create standing waves.
Standing waves are formed when a wave is reflected back and forth between surfaces n/2 wavelengths apart, where n is a positive whole number. The wave interferes with itself, creating static nodes, or areas where the amplitude is always zero, and antinodes, or areas where the amplitude varies between the absolute maximum and minimum values for the wave. For a sinusoidal wave, the spacing between any node to its nearest neighbour node, or antinode to its nearest neighbour antinode, is one half-wavelength.
Microwave ovens rely on the same principle. If you look inside your microwave, you will notice that the entire inside is made of metal, either solid pieces, or pieces perforated with small holes like on the door. (There’s usually also a rectangle that doesn’t look like it’s properly attached to the wall — that’s where you’ll find the antenna that produces the microwaves.) These are both very effective microwave mirrors. This not only shields the outside world from the microwaves generated inside the microwave oven, but also maximises the cooking efficiency by containing the energy in standing waves inside the microwave oven, and then rotating the food you are trying to heat so it passes alternately through areas of high and low intensity. Because of this, you can treat your microwave oven as a scaled down model of Hertz’s lab. The space is scaled down, and so is the wavelength of the radiation.
Maxwell not only predicted the existence and nature of electromagnetic waves, he was even able to predict their speed. The relationship between the wavelength, frequency and speed of a wave is a simple one: v = f•λ. Hertz was able to measure the wavelength and frequency of his mystery waves, thanks to being able to make standing waves, and thus he could easily calculate their speed. This speed was found to agree with Maxwell’s prediction, and also fell within the experimental error range of other scientists’ measurements of the speed of light.
There is a straightforward experiment you can do using your microwave oven to determine the speed of light using exactly the same principles Hertz did.
You will need:
- A microwave oven with a removable rotating plate
- A large, flat, microwave-safe plate or board
- Mini marshmallows. Please note that the resolution given by full-sized marshmallows is inadequate. Alternatively, you could use:
- Shaved cooking chocolate. (Note: please use cooking chocolate. Other forms don’t melt adequately, or burn. The author has tried this experiment with Flake bars, which not only burn but produce large amounts of surprising green smoke.)
- Cheese, of any sort. It will melt, sweat, or in the case of wrapped cheese slices, dessicate or burn quite nicely.
- Thermal paper, e.g. fax paper roll. Not recommended, because it is not delicious.
Step 1: Remove the rotating plate from the microwave. If the T- or X-shaped piece that drives the rotation is removable, remove this too.
Step 2: Spread your marshmallows (or alternative) evenly across your plate or board. Place the plate or board into the microwave, taking care to ensure it is level, and that it will not rotate.
Step 3: Run the microwave at full power for 30 seconds. If this has been inadequate to cause regions of heating and/or melting, without moving the plate, you can run for additional 10 second bursts until the desired effect is achieved. If you are using marshmallows, they will inflate during heating, but do deflate again fairly quickly once they are allowed to cool slightly. This is okay: once deflated, you will usually find they have shrunk and melted slightly, so it is still possible to tell the “hot spots” from the rest.
Note that the longer heating takes/the more times you need to reheat, the more sideways heat transfer there will be, and therefore the wider the “hot spots”. In the above photograph, some extra re-heating was performed to maximise the puffiness of the marshmallows for the photo, and you can see how wide the “hot spots” have become.
Step 4: Measure the distance between two nearest-neighbour “hot spots”. This is your λ/2 value. But how do you find the frequency? 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.
Step 5: Eat the melty marshmallowy mess.
In this demonstration, was found to be 7 ± 1 cm. f was given as 2450 MHz.
Therefore we can calculate:
c = f•λ
= 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
The true value of the speed of light in air, 3.0 × 10^8 m / s, falls within this range.