# Day 162: I Love Lucy, Toy Buggies, and the Wave Equation

It’s downright impossible to use slinkies to find the relationship between wave frequency, speed, and wavelength. (Well, unless you use standing waves, but that muddies rather than clarifies the physics at hand.)

But the relationship between candy frequency, conveyer belt speed, and candy spacing?

That’s easy with buggies, adding machine paper, markers, and a metronome.

The beeping you hear in the background is the metronome set to 60 bpm (1 Hz). The kids easily vary their marker frequency to 2 Hz (in video), 1 Hz, 1/2 Hz, etc. by counting. And they swap fast and slow buggies to change the conveyer (i.e., wave) speed.

With some thinking, many kids can arrive at the wave equation just contemplating the “I Love Lucy” scenario. And that’s what I’ve done in previous years. This is my first time trying it with the buggies first. A few kids were able to figure it out before doing any trials (“If I double the buggy speed, the dot spacing will double. If I double the frequency, the dot spacing will halve.”) but I ask them for experimental confirmation anyway.

The other part I like is asking them what relationship exists between frequency and speed. They easily see that none exists because the frequency is controlled by the metronome (ie, the source) and the speed is controlled by the buggy (ie, the medium). Tomorrow, I hope I can help them l make the same connection to wave frequency and speed.