# Harmonic Behavior Part 2

### Phase

We continue our discussion of harmonic waves, what relevant units of ampltiude are (I use dB and V) and how to disect Hz. We have a bit of a side discussion on how useful a second is when you're talking about a 800Hz wave and its 0.00125s cycle time. Oh hey, milliseconds! And for the extreme, microseconds. These discussions are great and all but again, do they understand what cycling really means? What does it look like? I had this idea of showing a video of cars and their out of sync turn signals or bulbs blinking or something. Sadly, the internet let me down. So I cranked out a couple animations:

I let them stare at it for a while, a few will shout observations. Then I ask a few questions: Which light has the highest frequency? The lowest? Where do the rest of them fall? A contentious debate arose about whether the top center or bottom left had the higher frequency (top center repeats every 3 frames, bottom left every 2).

Next, what does it mean to be out of sync?

Grasping a 180º shift is a little easier than a 90º but once I have them count the different colors the 90º image is going through they start to pick up on the pattern. We make some analogies to running/walking around a track in PE. Then I set them to work on the supplementary task. I present them with two signal waves that may or may not have different amplitudes, frequencies, and phase shifts. They graph one on top of the other and then describe. I leave a structure for the paragraph on the board. How can I expect them to write a proper mathematical observation if they've never seen what one looks like? Classic trap teachers fall in. I know how to do this and have for years and it's so simple, why don't you and your inferior knowledge and lack of experience not know how to do this already?

I liked the result, discussing phase shift as a unit of time I think helped with the translation aspect. When you're graphing sin/cos in terms of pi, I don't think the concept of cycling comes across as well because it's obscure and overly mathematician like to talk about distance or time in terms of pi. No one does this. Stop acting like they do.

### Tradition

If you want something that addresses the same concept but sucks all the fun out of the room, by all means, try the textbook version:

I'm so excited to try Exercise 55!

### Going Further

An idea on the table for next year is taking this project further. I think there's room in the schedule to start trigonometry a little earlier to leave room for more in depth exploration. If time weren't an issue, instead of hand feeding them amplitudes and periods, I'd have them take something like my blinking lights GIF and see if they could determine what the values should be for the picture. It needs some time to marinate though, I haven't quite determined how I would frame the questions. Something I'm really started to get frustrated with is how dependent a lot of them are on me to do the thinking, even with all these introductory tasks and things. This came to a head in a project on right triangles that followed a few days later.

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