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Physics Two Brain Dump: superposition, reflections, and standing waves.

September 22, 2017

With slinkies, it definitely pays off to take the time to teach students how to make (then practice) making good “pulses” of varying amplitude and width. Students who have a good sense of how to control wave pulses and trains are positioned to do better explorations. 

Last week I taught them how to make good pulses and they practiced, before going in to investigate the factors that do and don’t effect wave speed. 

After a day of some problem solving with spherical wave fronts, intensity, and the decibel scale, we returned to our wave model to extend it to

1. Multiple sources, and 

2. Finite media 

Wave Pulse Chicken

This led us back to slinkies to investigate superposition. Students made slow motion videos of wave pulse chicken. I wish I had all videos students made. They were awesome, and traversed a vast swath of scientific and aesthetic  territory. We shared our videos under the document camera, and talked about what we noticed and were wondering about. 

A brief lecture on superposition and a simulation preceded some clicker questions to practice. 

Superposition Clicker Practice 

First clicker question was an easier superposition one could do in your head. Everyone got it correct.

The second one was a long title bit harder to do in head, and so with discussion I modeled how to diagram it carefully.

The third question was much harder, and I told students ahead of time that we would first try to do it in our heads, and then go to whiteboards. Our first vote was all over the place, but students worked hard at their whiteboards and all reached same answer. Several students talked about it being fun to figure out how the waves superpose. 

Exploring Reflected Pulses 

So We add to our wave model the idea of superposition as a way to deal with multiple sources, and I pivoted to the issue of finite media with boundaries. Students were sent back to explore what happens when a pulse reaches the end of the line. Students observed the important features, and their was a very brief lecture on reflections. 

Pivoting to Sound Pulses and Echoes

We’ve been going back and forth between waves on strings and sound, so we pivoted to talk about sound wave reflections (echoes) and how to make a good sound pulse by snapping fingers. We practiced making good sound pulses and examined their pulse shapes with microphones.

We then observed reflections (echoes) ny snapping at one end of PVC tube closed off at other end with a whiteboard. This exploration allowed us to see echoes , and culminated in us calculating the speed at which the sound pulses traversed the tube. We got decent data, all between 320 and 350 m/s. 

Then we took a break. 

Wave Chicken with Reflected Waves

Back from Break, students were sent off to play “pulse chicken” with reflected waves–and to figure out how to constructively and destructively interfere with it. Students had fun with this, and had gotten really good at creating pulses that would cancel out. 

This “naturally” led us to standing waves, which I motivated in part by switching from sending wave pulses to sinusoidal waves. We explored a simulation to look at how traveling sinusoidal waves superpose to create a “standing wave effect”. 

Exploring Standing Waves

Students were tasked with trying to make standing waves with slinkies. Students struggled with it, which was good. They struggled exactly because only certain frequencies work. For many groups, I eventually modeled how to make a standing wave, but I always did it with my eyes closed. The trick of keeping your eyes closed helps them notice that it’s about “feeling” the right timing. Only the right timings will create standing waves. 

Students were then successful at making standing waves of their own. We summarized our findings and introduced the modal naming conventions. We practiced with clicker questions, naming and identifying wavelength of various standing waves. 

Concrete to Abstract: Inventing Equations

Then students were tasked with drawing first six modes on a string of 120 cm length. They had to determine wavelength of each, and then without drawing see if they could determine higher order modes as well. Students were then pressed to invent an equation. Most students invented wavelength  = 2L/mode, or wavelength = L / (m/2).  Mostly while circulating I helped connect rewrite this as m * half wavelength = L.  Each picture shows either 1, 2, 3, or 4 … half wavelengths fitting inside L. Mode number tells us how many halfwavelengths are needed to span the length.

Guitar as Example and Teaser

The day ended by looking a guitar string by oscillating in slow motion, and under different harmonics. The final teaser was to look at the frequency spectrum for gently tapped tuning fork vs a harshly plucked guitar string. 

Next week, we return to problem solving with standing waves. 

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