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Intro to Waves Sp14 Reflection

March 19, 2014

Overall I think the Intro to Waves unit in Physics 3 went smoother this semester than last. Quick recap…

What’s New
The biggest changes are two tutorials that I wrote. We started on Day 1 with an Intro to Traveling Waves tutorial. My goal was to get students to think about units (the argument of a trig function always has units of radians) and use their knowledge that one cycle of a trig function corresponds to the argument increasing by 2Pi to construct a wave function for a traveling periodic wave and to construct equations relating wavelength, angular wave number, wave speed, etc. I also tried to get students to see the value in graphing y vs. x for a given value of time and/or y vs. t for a given value of x. Mainly I was trying to give students some tools for solving problems rather than flooding them with a bunch of seemingly brand new equations like the textbook does. I think this worked OK, but there are certainly sections where I need to improve my wording and I need to make more explicit call backs to these tools throughout the unit.

The other tutorial I wrote was on 1D standing waves. Last semester I had students sketch y vs. x plots of standing waves on strings and in air columns but I largely failed in communicating that these sketches are a great way to solve problems rather than memorizing equations. My goal for the tutorial was to wrap the entire discussion around these sketches.

I started by having students play with the PhET wave on a string sim to time their wave pulses so that the pulses were always on top of each other and to relate the time between pulses to the time it takes the pulse to travel down the string and back. I did this to introduce the idea of multiple waves interfering and that if the waves are timed just right, we can keep increasing the size of the peaks rather than increasing the number of peaks. However, I’m not sure this was very successful.

From there, the tutorial introduced the idea of boundary conditions and had students draw standing waves based on drawing sine or cosine waves of various wavelengths that satisfy the boundary conditions. Then from the sketch, students relate wavelength to the length of the medium and relate wavelength to frequency using v=lambda*f. This part was largely successful as judged by student success on the standing wave problem on the exam. (I’ve also made using diagrams to construct equations one of the course-level learning goals.)

The other main change for this unit was the addition of a lab on 2D standing waves on Chladni Plates. This was added after several students last semester expressed an interest in YouTube videos showing Chladni Plates. We currently have one setup (one square plate and one circular plate) so students worked in large groups. They used mechanical oscillators connected to function generators to drive the plates at various resonances. Students found resonances by exploring and for each resonance they recorded the frequency, a rough sketch of the nodal lines, and for the circular plate, the radius of each nodal line. I provided students with the two dimensional wave function (A bessel function in r times sines and cosines in theta and t) and explained (maybe too quickly) how the boundary conditions are satisfied by the wave function. Students then used WolframAlpha to plot the radial zero points of the wave function for different standing waves and compared this to their measured radii. They also used Chladni’s Law to calculate the expected frequencies of the standing waves and compared these with their measured frequencies. I need to think more about how best to bridge our discussion between 1D and 2D, but students enjoyed the lab, the measurements and predictions were in pretty good agreement, and students got to see standing waves that weren’t sine waves.

The Chladni plate lab took the place of a lab on Fourier Series which I’m still trying to fit into this semester.

For electromagnetic waves, I revised my learning goals for unit 1 to focus on applications of intensity. The idea and mathematical definition of intensity is new to students in Physics 3 and light offers much more varied and interesting applications than sound waves so I’m going to focus in unit 1 on applying the concept of intensity to light waves. By this I mean relating intensity to 1) the total amount of EM energy passing through some area in given amount of time, 2) the power of an EM signal various distances from a transmitting antennae, and 3) the radiation pressure exerted on an object that is absorbing or reflecting light. I like these types of questions because they have interesting applications (solar cells, solar sails) and they can be solved just starting with Intensity = Power/Area and then using Physics 1 concepts to write power in terms of energy or force. They essentially become dimensional analysis problems.

A Wonderful Surprise
I showed students a video from Mythbusters of inhaling helium and inhaling sulfur hexaflouride and how each affects your voice. We watched this video fairly early in the unit just after introducing sound waves and looking at how the medium affects the speed of sound. After some prodding from me for students to provide a deeper explanation than what is given by Mythbusters, students realized they didn’t really understand what was happening and started proposing lots of interesting ideas. Students provided their own arguments for why frequency will stay the same and wavelength will change when a wave changes mediums (something I haven’t had students do in the past). They also spent some time outside class looking at websites trying to understand how vocal cords work and why having a different gas in your throat would affect your vocal cords (it doesn’t). I realized that I didn’t really understand how vocal cords work and did some researching myself and came across a nice TPT paper (also, here is a nice ScienceGeekGirl blog post on this topic) I shared the paper with the students and lots of our subsequent discussions about standing waves and resonance were framed around understanding what our vocal cords do, how we make different sounds, and what the heck is happening in the Mythbusters video. What I originally envisioned as a one-off amusing video turned into an extended discussion that lasted several class periods and motivated several future topics.

Still Missing
Like last semester, I also did not end up doing anything with sound levels and decibels despite being on the learning goals. I want to write an at-home activity related to this, but I haven’t had time yet. Also as mentioned above, the Chladni Plate lab took the place of a lab on Fourier Series which I still want to do and I think really needs to be done in class. I’m OK not doing the lab before the Unit 1 exam but I do want to fit it in somewhere for its own sake and also to give us some conceptual footing on which to think about the uncertainty principle in Unit 3.

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