Your Microwave Is a Physics Laboratory, You Will c!

We have reached a point where physicists’ experiments can be rarely realized without being very knowledgeable about the subject matter or having expensive, high-precision equipment, not to mention the often vast amount of time needed to finally obtain results. That is why I am always giddy with pleasure when hearing about an experiment which can be easily done in a short time by using just household objects. Here and now I want to drop a line about such a DIY experiment and tell you something about your microwave oven and how it can be used to measure the speed of light.

I have known this experiment for a long time already, but never thought of writing a blog post about it since it got kind of lost in the back of my mind. It only came out of hiding recently when I stumbled upon an article on “From Quarks to Quasars”. There, Joshua Filmer explains how to measure the speed of light with an accuracy of 97 to 98 percent in five easy steps (including pictures!).
I recommend reading his text before continuing here (don’t worry, I’ll wait patiently) in order to exactly know what I am going to speak about.

In short, all you have to do in order to measure the speed of light – or, how physicists affectionately call it: c – with your microwave is to put a hot dog in it before turning it on for some time. It is essential to remove the turning plate in advance so that the hot dog remains stationary while being heated. If you are short of hot dogs, you can also use a bar of chocolate or a plate covered with grated cheese, etc. (Although I haven’t tried the experiment myself, I imagine chocolate or cheese actually doing an even better job than a hot dog, but if I’m wrong, just leave a comment and teach me better.) Then, well before the whole stuff is fully cooked, just take the hot dog (or whatever you put into it) out of the microwave. You should be able to see some sections which are melted and others which are not. Measure the distance between two melted parts and put it into this formula and obtain a value for the light speed c:

c=2.45\times 10^9\times 2\cdot\text{(distance in meters)}

The relation your are using here is c=f\cdot\lambda, i.e. (light speed) = (microwave frequency) times (wavelength). Since the speed of light c is always constant, it describes a simple connection between the (electromagnetic) wave’s frequency f and its wavelength $\lambda$: The higher the frequency is the smaller the wavelength has to be, and vice versa.

So far, so good. Up to this point, everything has been carried out in Joshua’s text. However, it just tells you what to do and how to put the numbers into the formula, leaving aside an explanation for why there are melted and unmelted places in the first place and all the cool physics behind the experiment. Let me try to catch up on that now.

A microwave oven is, on closer examination, an interesting piece of technology. It creates an electromagnetic field inside the chamber which oscillates incredibly fast. The rapid switching of the field happens 2,450,000,000 times per second. (This is the number we have used in our equation above: f=2.45\times 10^9 Hz.) This oscillating field causes the water molecules in the food, which have something like a positively and a negatively charged end due to their molecular structure, to spin and wobble like crazy since they constantly try to align to the oscillating field. All the wobbling result in even more wobbling and finally in an increased average speed of all the particles in in the food – which is nothing other than an increase of the food’s temperature. (If you want to get a feel for how fast particles in stuff like air move and how often they bump into each other, see my previous post.)

Standing waves in a microwave oven's chamber

For the sake of simplicity, let’s just consider a one-dimensional “cross-section” of the microwaves in the oven chamber. The waves are directed into the chamber from the right and subsequently spread within it. But only those waves (or multiples thereof) which exactly fit between the walls become prevalent.
(Picture presumably taken from the EngineerGuy video (link at the end). Source: geek.com)

However, the essential physical feature for our experiment is that in the oven’s chamber only those (micro)waves form and become dominant whose wavelengths (or multiples thereof) exactly fit between the walls. Thus, a complicated pattern of standing waves emerges within the chamber. It is quite hard to predict it, but it can be easily made visible by putting hot dogs, cheese, chocolate, etc. into it: At those places where all these superposing waves interfere in a constructive way (i.e., amplify each other), the oscillating field is stronger and therefore the food gets hot there faster. (The turning plate’s purpose is the compensation of this very effect: By rotating the food it ensures a uniform heating. Now do you see why it was crucial for our purposes to prevent the plate from spinning?)

(By the way, there are of course many other possibilities for visualizing (not just electromagnetic) standing wave patterns – and mostly it just looks cool! I strongly recommend watching the flaming 2D Rubens’ Tube aka the pyro board, the resonance modes of sand on an oscillating plate, or the standing waves of a vibrating string.)

So if you now measure the distance between two extra-molten sections, you actually pin the distance between two antinodes or, in other words, half the wavelength of the oven’s microwaves. Just take this value and put it into the above formula and you will get a result for the speed of light, which is about 300,000,000 m/s. (Of course, you can also calculate the frequency of your microwave if you use the known value for the light speed. In this case, you just have to put the measured distance (in meters) into the formula f=\frac{299,782,458}{2\cdot\text{(distance)}}.)

Isn’t it cool that you can determine the enormously fast speed of light with an error of only a few percent by using just household items and simple mathematics?!
Let this experiment remind us again that physics isn’t necessarily something that is solely done by people with smart brains and in laboratories, but that it is everywhere, directly affecting our everyday lives, and that everyone can take part in exploring the world and asking nature about herself by performing experiments.

 

As a last point: If you are interested in how the microwave oven’s rapidly changing electromagnetic field is created in the first place and which components it is generally made of (or if you just want a short summary of this text including a demonstration with a plate of grated cheese), click here and watch this video by EngineerGuy – it takes five more minutes, but afterwards you’ll be a microwave pro.😉

 

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