There are many ways to teach the inverse relationship between wavelength and frequency of photons. Videos. Slinkies. But I think this one is the easiest and most visual way for students to remember. Running. I teach my grade-level students about light during the cross country season, so there is an easy tie-in. Here’s how I do it.
My close friend Jeremy is 6’9”. He and I both ran cross country together. Take a moment to revel in the thought of a 6’9” guy running in cross country shorty-shorts. Glorious, isn’t it? There was a race where Jeremy, who usually beat me soundly, had the flu. We ended up running next to each other. We were travelling at the same speed, just light photons of electromagnetic radiation through a vacuum.
At this point in the story, I ask them about who had to take more strides. Since I am only 6’1”, it is obvious that in order to travel at the same rate my stride frequency has to be greater. Especially since my legs are so much shorter. Short stride length must be paired with a high stride frequency in order to match the speed of a high stride length with a low stride frequency.
Make the story even more ridiculous. The worlds tallest man and the worlds shortest are racing and it is a tie. In order to go the same speed (which I describe as c, 3x10^8 m/s) the photon with a short wavelength must take so many more steps per second (higher frequency). This helps the students visualize the inverse relationship between wavelength and frequency.
The great thing about the equation c = λν is that if you put little running shoes on the lambda, you get a visual reminder of which variable represents wavelength. It shows how long of a step the running lambda is taking. This honestly helps some kids who can struggle keeping track of all the variables.
This simple little story is an easy way to introduce wavelength, frequency and the speed of light. Hope it helps. Or at least inspires you to go find your shorty-shorts and get out there for a run. Me? I think I will sit this run out.
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