## Modelling the Doppler Effect

I have recently started reading about modelling instruction and have decided to incorporate it into my teaching as much as I can. Today I tried using this approach to teach the Doppler Effect and my students said they preferred it to the old way.

Before continuing, be aware that I am a complete novice at this: modelling workshops seem to only be happening in the States, whereas I teach in Germany. This means all the knowledge I have gathered on the topic has come from reading blog posts such as this one (thanks to Kelly O’Shea for posting that). Any suggestions on how to improve will be more than welcome.

I decided that looking at waves in water may be the easiest way to see the Doppler effect in motion. Unfortunately, I do not have a proper wave machine, so I had to make do with two big plastic boxes. I tried several methods of producing waves and I ended up sticking with the good-old “stick your finger in the water.” The waves were hard to see, so I tried several adjustments until I found that turning off the lights in the room and illuminating the surface with a table lamp made the wave fronts quite visible.

Anyway, that was the set-up. The students came in and I put them in two groups of 3 (I have very few students), one for each box. I scaffolded instruction as follows:

1. First I asked students to dip their finger on the water and observe what happened (a wave is created.) Then I asked them how they would measure the speed of the wave (take two points, time how long it takes, divide). Finally, I asked them to measure the speed of the wave.
2. Then I asked them whether tapping harder would change the speed. Some were not sure, so I told them to check if it did (it doesn’t). Then I asked them whether tapping more frequently would change the speed. Again, some were not sure, so they checked (it doesn’t).
3. Then I asked them whether moving the finger forward as they tapped would change the speed of the wave. In this case, there was quite a bit of debate. They finally made some measurements and agreed that it does not. So I asked: “what is the only thing that affects the speed of the wave?” They all replied that it had to be the medium and nothing else. Finally: I’ve struggled with this misconception for a while.
4. Once that was clear, I started preparing the grounds for the Doppler Effect. I first asked them to measure the wavelength they got by dipping their fingers at intervals of one second. Students used their phone to take a picture and compared with a ruler placed across the box.
5. Then I asked the students: will the wavelength change if you start moving your finger forward at a constant speed but tap at the same intervals? They all said “yes.”
6. After that, I asked students to measure the wavelength they got if they moved their finger at a speed of 1 cm/s, still tapping the water once per second.

This was the more practical part. Then came the attempts to make a model. Now, I am pretty sure there is a better way to do this and, if anyone knows it, I’d be really grateful if they explain it in the comments.

1. First, I asked the students to go to their small whiteboards (I don’t have big whiteboards yet, they’ve been ordered though) and model the situation. I reminded them that a model is just a simplified representation of reality where only the relevant characteristics remain. I told them models could be graphical or mathematical, but that probably at the beginning you want to stick to drawing.
2. Students started making their models. This was their first time to do so, even though we had talked about this before. It was surprising because many of them actually drew the lamp or the shape of the box. It was also surprising to see that all of them opted for a sine-like drawing of a wave (as seen from the sides) rather than drawing the wave fronts, which is what I had expected.
3. I reminded students that only relevant characteristics should be there. “Will the lamp affect the wavelength you get when you move your finger?” “No.” Etc. Then I tried to prompt them away from their 1-dimensional wave models and towards a wave front drawing.
4. Once they had that, I asked them which quantities would mater if we wanted to do any calculations in that situation. They almost unanimously responded “the time between the taps, the speed of the wave and the speed of the finger.” I made sure that they remembered that “the time between taps” was the period.
5. After this, most of them reached an equation which looked like:
$\lambda_{f}=T(c-v)$

The last part was really just beautifying the equation, replacing everything with frequencies. However, I had to introduce the notion of an emitter and a receiver, which I think I should have done earlier, though I am not sure how it would have fit into the initial picture.

We had to leave it here. Of course, it would have been great to talk about both moving sources and receivers, but I am not sure how easy that would be to show in the lab. Maybe simulations are the way to go for this one. If anyone know of a great strategy for that, please let me know in the comments!

We spent the last five minutes taking about some situations where this may be helpful (I mentioned finding out the speed of cars and of galaxies, for instance). Students seemed fascinated by what happens when you’re travelling at exactly the speed of the waves in the medium. They wanted to know what you would hear if you were travelling at exactly the speed of sound (outside the cabin, not inside!) I conjectured you’d hear nothing (since you’re riding with the wave, the frequency is zero and therefore outside our hearing range) but your ears would implode from the massive pressure. Was I right?

All in all, students were very positive about the lesson, saying it had given them a much more intuitive understanding of the process. This encourages me to keep pursuing this further, even though I am not sure how I can manage it when, for example, tackling the electric and gravitational fields. Mechanics and thermal physics lend themselves really well to modelling, but I am still at a loss about how to approach topics like fields or quantum mechanics.

## About the author

### Eduard Arroyo

I am passionate about transmitting passion, both in physics and education in general.

## 4 thoughts on “Modelling the Doppler Effect”

1. This sounds awesome. I’m happy to talk about how to incorporate more Modeling in your pedagogy if you’d like. You can find me on Twitter or send me an email. 🙂

1. Hi Kelly,
Thank you so much for replying! I have to say your blog has been my main source of information and inspiration to start this. Thank you so much for offering to help!

2. At this time it seems like WordPress is the best blogging platform out there right now.
(from what I’ve read) Is that what you’re using on your blog?

1. Hi,
At the moment, it is, especially if you use the self-hosted version. It has lots of options and it’s very customizable with plug-ins.

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