Each semester when I look back my slides there are little gaps from days when I don’t use slides or fuzzy records about whether some things took one or two days. I’m continuing my weekly record of daily activities.
Looking at our first homework assignment, students are still struggling to assign map directions to celestial sphere diagrams and have trouble comparing observers at different latitudes. I went through a few sketches on the board showing an observer on Earth, drawing the corresponding horizon, and showing how to determine NSEW on the horizon. I wrote a set of review questions to be answered online which are hopefully helping.
We spent the first half of Tuesday reviewing some Moon phase concepts from last week and checking some of our results from the Cause of Moon Phases tutorial homework. This is the first tutorial in which both students in a hypothetical conversation having mistaken ideas so we talked through what was correct and what was incorrect in each student’s statement. Last 20 minutes was spent with students working on the Predicting Moon Phases tutorial about determining when different phases rise and set. Students struggled with this a lot – they weren’t drawing diagrams and weren’t sure how to determine times.
Thursday, I spent the first half of class going through some tutorial questions as a class drawing diagrams and talking about how to use an observer’s location relative to the Sun to determine approximate time of day for the observer. Students felt much more confident after this discussion and did a pretty good job finishing the tutorial on their own (although I still had to encourage students to draw diagrams for harder questions). I don’t know right now if the class discussion would have been beneficial on Tuesday, or whether starting the tutorial cold and letting students realize they had difficulties primed them to be more engaged during the discussion on Thursday. Preparation for future learning?
This week’s lab covered angular size and parallax. We practiced holding a coin at a position where it was the same angular size as an object in the classroom and set up ratios for the distant object. This worked OK, but showed students had not engaged with the pre-lab as much as necessary. After the practice, we went outside with eclipse shades and did the same thing with a rubber band and the Sun. We also tried carrying cardboard circles to a distance at which they appeared to be the same angular size as the Sun, but those ratios tended to come out with too large of a distance to diameter ratio.
The parallax part was done inside and involved students spreading out in a right triangle and using their hands to estimate angles in the triangle and then compute distances. This was a little confusing for students who was measuring what and how this related to our conceptual introduction of parallax.
Monday and Wednesday we talked about the microscopic meaning of entropy working through a small toy example for which we can explicitly denote microstates. I took a homework from last year and rewrote it to be a take-home exam problem for this year. The problem has students use Excel to calculate microstates for slightly larger systems and see how the most probable state compares to the expected equilibrium condition (better agreement as the system gets larger) and also introduces how to define temperature in terms of the derivative of entropy with respect to internal energy.
We don’t really talk about macroscopic entropy. This is my decision, but I’m not sure how I feel about it. I like the microscopic entropy because I think explaining why equilibrium exists and why heat flows from hot to cold is amazing. However, macroscopic entropy would be more useful for calculations and for connecting to entropy discussions in chemistry.
Friday we talked about heat engines. We don’t calculate that much with heat engines. Mostly we write the first law of thermo for heat engines, define efficiency, and show that if a Carnot engine has constant entropy, then efficiency can be written in terms of reservoir temperatures. RealTime Physics has a nice activity on heat engines that I wanted to do, but I didn’t get organized enough to work this into lab (which I’m not teaching) and I couldn’t fit it into lecture.
Heat engines marks the end of our thermodynamics unit. I feel like this unit is under-motivated. I put a lot of work into connecting ideas and trying to make concepts feel intuitive, but I think I have a lot to do to connect more to applications and engineering aspects.
Monday we introduced sound waves focusing on why sound waves are longitudinal, what causes pressure variations, and why Pressure Variation vs. Position and Avg. Displacement vs. Position graphs are phase shifted from one another. We don’t do much with the speed of sound.
Wednesday we started by trying to use function generators and speakers to set up standing waves in our ear canals. This did not work too well. I didn’t give any instructions other than to slowly increase the frequency from 1 kHz to 10 kHz and see if they notice anything. These are higher frequencies than students are used to and the resonances are narrow so mostly students missed the effect. I think this works better if we talk about what happens and at what approximate frequencies before the experiment.
After the experiment, I talked about how a gas particle has no room to move if it’s next to a closed wall and hence displacement must be a node at a closed wall and built up all other boundary conditions from there. Then I had students sketch a few different standing waves for either pressure variation or displacement to check their understanding. Still some confusion about determining the harmonic number (which I refer to as simply the “first possible”, “second possible”, etc. standing wave).
In lab, we set up standing sound waves in tubes partially filled with water. This works pretty well, except that students mix up what length corresponds to the effective length (with the end effects included) and what length corresponds to the length of air-filled section of the tube.
We also looked at a video of vocal flaps vibrating to see that 1) vocal “chords” aren’t actually chords and 2) the vibration is more messy with various frequencies than you might expect. I used the video to argue that breathing in helium does not change the vibration of the flaps and so we still have unanswered questions regarding the Mythbusters video. After the tube experiment, I try to get students to listen to multiple simultaneous frequencies through a pipe for which one of the frequencies is at resonance. I still haven’t found a great way to do this. I try two speakers driven by two function generators and I try listening to a square or triangle wave through the tube and without the tube. I can tell some differences in pitch but students mostly just notice a change in volume. At the end of lab, I connected the experiment to the Mythbusters video and talked through a full explanation for why helium changes your voice. This discussion was too much of me. I need a better experiment and a unit-long structure for this question that helps students connect all the necessary concepts.
Students had worked on the Ecliptic tutorial over the weekend so we started Tuesday with some follow-up clicker questions and I asked for their responses on a few of the tutorial questions. Later that afternoon I found the Motions of the Sun simulation from Nebraska that helps illustrate the Sun’s motion along the ecliptic versus the Celestial Sphere’s daily rotation.
After finishing the ecliptic discussion, we moved into Moon phases. On Tuesday, students did a brief activity where you hold a styrofoam ball on the end of a pencil, turn off all the overhead lights except a single incandescent lamp in the front of the room, and students observe how much of the ball is actually lit and how much of the lit part can they see from their angle as they move the ball around the head. Students generally got the idea but it didn’t work as smooth as I would have liked because 1) I had to goad students into actually doing it. Students worked in groups and most groups seemed content to have a single person actually view the styrofoam Moon from different angles. and 2) For a class of 30 students I set up 2 incandescent bulbs, one on each side of the room, but this created a lot of ambient light so the phases were not as easy to see as I would have liked. We used the activity sheet from Hands on Science at Texas for this activity.
On Thursday we continued the Hands on Science activity that involves Moon collars with several Moon locations marked and a ping pong ball colored half black to represent the Moon. Students again worked in groups (you need more than two hands to hold everything) to view the ping pong ball at different positions and match each position to one of the Moon phases with names on a table I handed out. This went pretty smooth (again I had to push students to have everyone in the group wear the collar explaining that they will be much more likely to remember how this worked on an exam if they actually experience it rather than just watch). We continued using the Hands on Science activity packet which guides students through questions about where the Moon is in its orbit when the lit section visible from Earth is growing vs. shrinking, when the Moon is closer or farther from the Sun than the Earth, etc.
At the end of class I asked students where the full Moon phase would go on their collars (this phase is not one of the listed positions) and then asked if this position should be a full Moon or an eclipse. Students agreed that eclipses don’t happen every month so it should be a full Moon. I agreed but said that the way we did this activity, their position would correspond to a lunar eclipse. I explained that the Moon’s orbit is tilted relative to the Sun-Earth plane and illustrated how tilting the collar would put the Moon behind and above Earth. I also (for fun) briefly discussed the phrase “dark side of the moon”. Students are working on the Causes of the Moon Phases tutorial for homework.
We started by finishing our Scale Model of the Solar System activity from last week. Last week, students cut out scale paper representations of the Sun and each planet. This week we started by taking students outside with each student holding a sign indicating what object (Sun, a planet, Pluto) they represented and measured them out to represent a scale model of the planet spacing. Using the scale they chose last week, this model spanned about 23 meters with the first few planets a little too close for students to squish together well.
Our lab this week was a variation on Eratosthenes’s experiment to measure the circumference of the Earth. The pre-lab starts by looking at shadows cast by vertical objects in different locations and explains Eratosthene’s original experiment and then leads students to think about the altitude of the Sun at different locations (how we do our experiment). In lab, students use a USNO site to look up the altitude of the Sun at different locations at the same time. I tell them to use Austin, TX and Fargo, ND to start which gives very good results and then ask them to repeat the experiment for two other pairs of cities that line along a primarily North-South line. This lab is based on a tidbit in Great Ideas for Teaching Astronomy (a really fantastic book of brief ideas suitable for a class discussion or that can be built into entire activities).
On Monday, I introduced different types of ideal gas processes and set students to work in groups on a question asking to find final temperature, change in internal energy, heat transfer, etc. for a constant pressure process. This took the entire period, but students did a good job in their groups of figuring out how to use our starting points (ideal gas law, integral definition of work, 1st law of thermodynamics, internal energy of an ideal gas) to build up solutions. I gave students a second problem to try at home, but hardly anyone worked on that between Monday and Wednesday.
On Wednesday, we did some clicker questions on adiabatic and isothermal processes that led to very engaged group discussions about whether heat transfer has to be zero for isothermal and whether temperature has to be constant for adiabatic. I demonstrated a fire syringe and asked students how we might describe what happens to the gas and why the cotton catches fire. That discussion went pretty well with me pushing a little bit for more explanation but contributions from different students building up a fairly complete description. We ended by introducing a cyclic process and thinking about how to determine Q, W, and &\Delta;U for each segment and for the process as a whole.
On Friday, I was going to talk more about degrees of freedom and how quantum mechanics leads to a breakdown of the equipartition theorem (or a freezing out of certain degrees of freedom) at certain temperatures but decided to write this into a guided homework activity instead. We’ll see how the homework went come Monday. In class, we worked on the ideal gas tutorial from Washington. Students were engaged and discussing in their groups, but they struggled more than I anticipated and we did not get as far as I had hoped. We don’t have a separate recitation section for this class and I’m trying to figure out where to fit in some of the tutorials. I can probably fit them into lecture, I just have to plan better and reorganize a little bit what I do in class and what I ask students to do on their own before coming to class.
I felt like Physics 3 went really well this week. Last semester, I wrote a tutorial to try to guide students through thinking about standing waves on a string. It starts by having students use the PhET Waves on a String simulation to figure out how to time pulses so that each pulse constructively interferes with the previous pulse resulting in a single larger pulse. They do this for one and two pulses on the string determining an expression relating the time between pulses to the length of the string and the wave speed. Students then look at the Walter-Fendt standing wave simulation to help us visualize incident and reflected periodic waves and how their superposition works. Finally, the tutorial introduces the idea of boundary conditions, how to use boundary conditions to sketch possible standing waves, and how to use the sketch to determine wavelength and thus frequency.
Last semester, lecture and lab were in the same room and every period students had access to computers which is necessary for students to complete the tutorial. This semester, our lecture room only has an instructor computer so I decided to change the tutorial to more of an interactive lecture demonstration. This worked very well. I would ask students to think about how to time the pulses and then try their suggestions. We discussed coming up the equations and the sketches together, and I was able to alleviate some confusions that arise due to poor wording in the tutorial. Students still worked through the tutorial, but we did it as a class and finished the tutorial (standing waves on a string with two fixed ends) in 50 minutes.
On Wednesday, I broke the class into three groups (it’s only 8 students this semester) and gave each group 25 minutes to accomplish one of three tasks: 1) calculate the expected standing wave frequencies for an experimental setup and use the setup to test their calculations, 2) use the PhET simulation to determine pulse timing for the case of one free end and to use this to try to determine what would be needed for two free ends, or 3) sketch the first two possible standing waves for the case of one free end and the case of two free ends. Students worked in their groups while I floated around offering minimal suggestions and then we spent the last 25 minutes of class with each group sharing their results with the rest of the class. Students didn’t take notes on other groups’ work so after class I wrote up a summary of everyone results to post on Canvas. Each group succeeded in their task and everyone seemed to be enjoy the class (some students even saying so explicitly). I think this worked well because everyone’s task was just different enough from what we did on Monday that students felt like they knew enough to succeed yet had to bring together enough ideas from previous classes that they felt that they were discovering things on their own. It seems like a less-than-ideal classroom setting actually helped me stumble onto some more effective ways of covering these topics.
In lab, we built Sound Sandwiches and used our new ideas about standing wave frequencies to think about why certain adjustments lead to changes in volume or frequency. Students look at the Fourier series for their Sound Sandwich and see multiple frequencies from which they are asked to determine the fundamental frequency. They are then asked to experimentally determine the fundamental frequency they would expect for their Sound Sandwich based on properties of the medium. My thought, and what students did, was to use a force spring to measure tension in the rubber band, measure the linear mass density of the rubber band, measure the length of vibrating rubber band, and use f = v/2L. This actually doesn’t work. It works well for predicting the lowest frequency of the rubber band when you stretch it between your fingers and pluck it, but it does not work well for predicting the lowest frequency on the Sound Sandwich. I do not know why. We talked about the possibility that maybe the Sound Sandwich only produces certain harmonics and so what we though were fundamental, 1st, and 2nd harmonics are actually more like 3rd, 6th, and 9th harmonics. A student brought up the possibility that the rubber band might not have uniform tension due to the way it is clamped and so maybe measuring tension in a free rubber band stretched to the same length doesn’t work well. This is an open question for us. The last part of the lab asks students to relate these ideas to guitars and explain why different strings produce different pitches, turning the tuning pegs changes the pitch, and why pressing down on a fret changes the pitch.
Forgot to mention that we started lab with a discussion of the Mythbusters Fun with Gases clip (introduced on Day 1). We listened to Adam’s explanation in the video and talked about what makes sense, what assumptions are involved in his explanation, and what questions we might still have. I used this to motivate doing the Washington tutorial on transmission and reflection as homework. The tutorial looks at wave pulses transmitting from one string to another so I assigned the tutorial with the overarching question of what variables (wave speed, wavelength, frequency) change when the sound passes from helium in Adam’s throat to air in the room.
No classes on Monday due to Labor Day.
Students worked through the Motion tutorial over the weekend so we spent Tuesday discussing clicker questions related to the daily motion of stars through the sky and how to relate this motion to the Celestial Sphere. On Thursday we worked through the Seasonal Stars tutorial in class and started the Ecliptic tutorial which students are completing for homework. I also spent a few minutes each day talking about how to use the Rotating Sky simulations from Nebraska.
Students are struggling some with interpreting diagrams and thinking three dimensionally. I’m accustomed to thinking of “into the page” and “out of the page” as potentially relevant directions when looking at a diagram due to physics. I need to remember that thinking about these directions is largely new to these students.
This week’s lab focused on scale diagrams and why it is unfeasible to design a scale diagram of the Solar System. I split the lab in two and had one half look up planet sizes and decide on a scale to use such that they could cut out paper circles representing each planet to scale. The other half of the class looked up planet-Sun distances and decided on a scale to use such that they could spread out to scale in the Quad. Groups then shared their results and each group calculated one of their distances using the other group’s scale to see that this results in unreasonably large or small scaled distances. Students also read a short excerpt from Bill Bryson’s Short History of Nearly Everything in which he talks about the scale of the Solar System and discusses the Oort Cloud and how the Solar System extends far far beyond Pluto.
This lab wasn’t really an experiment, but we will be using diagrams all semester that say “Not to scale” so I felt like we needed to talk about what they means. In addition, I wanted to make the scale cut outs and a video of walking the scale spacing for lecture since I didn’t have a good way to do this activity in a lecture room with 30 students.
I remember a Colorado paper showing that students explore PhET simulations more thoroughly and do a good job of making relevant observations if you let the students explore freely rather than giving detailed instructions. With this in mind, I’m trying to open up our use of simulations some. I started Wednesday by handing out laptops (1 laptop per 2 students) and gave students 10 minutes to explore the Gas Properties simulation with instructions to see what the controls do and what they find interesting. Walking around, I heard multiple groups notice that if you pump in particles and then increase the gravity the temperature increases. I wrote this observation on the board and said we’d come back to this at the end of class. I then gave students 5 minutes to find as many ways as possible to increase the pressure inside the box. I recorded students’ findings on the board and showed that each finding agrees with the Ideal Gas Law. We then discussed the microscopic origin of gas pressure (particles colliding with container walls) and talked about how this can explain why each change students identified results in an increase in pressure. We finished by talking about the microscopic meaning of temperature and introduced the equipartition theorem but did not have time to explain “degrees of freedom”. At the very end I returned to the gravity-temperature link and discussed this in terms of a sudden addition of gravitational potential energy which is then converted to KE (related to temperature) as the particles fall.
On Friday we talked a little about degrees of freedom focusing for now on translational motion. I walked through an example using the Equipartition theorem to calculate the average velocity of a nitrogen molecule in the air. Our result (~500 m/s) is noticeably higher than the average speed in Gas Properties for the Heavy Species (~425 m/s) so I pointed out that Gas Properties treats the box as 2D and thus there is only 1 kT rather than 1.5 kT contributing to the kinetic energy. I used the simulation to demonstrate that decreasing the volume results in an increase in temperature and (overly?) guided students to view this in terms of work and introduced work done on the gas as the negative integral of pressure with respect to volume. I ended by introducing the 1st law of thermodynamics.
I need to work on timing for these topics. I don’t like introducing a big important idea at the end of class without sufficient time to discuss. I also need to think about what ideas I want us to develop together in class, and what ideas students can be introduced to on their own outside of class either through reading or working through a guided assignment. Wednesday felt very productive but Friday felt like some of that would have been better delivered outside of class. Too much watching me and not enough of students being in the driver’s seat.
Last week was largely exploratory with students working together on tutorials and trying to answer various questions in lab so we spent Wednesday summarizing some of our findings and making sure we were all on the same page. This class didn’t feel that exciting but it ensured me that everyone came out of week 1 with the right ideas. Also the first three classes were almost completely devoid of direct instruction so the students might have been in a place to want a little bit of verification (I’m not sure if this is true).
We spent the first hour of Thursday’s lab working on the UW tutorial on Superposition and Reflection. Students saw superposition of wave pulses on Slinkies in the first lab but they didn’t have a formal definition so I lectured for about 5 minutes and then set them to work on the tutorial. Students also recognized coming out of last week’s lab that there were questions on the Mechanical Waves Conceptual Survey about how asymmetric pulses reflect that they did not know how to answer from the previous lab alone. The tutorial went pretty well with students needing some guidance on adding partially overlapping waves graphically but getting the hang of it once I got them started.
The rest of lab period was spent doing a “lab” on how to use the function generator and oscilloscope. I’m a little torn on this lab. The goal is primarily on the basic use of this equipment (there’s a second part to the lab but with the tutorial no one go to it). I think the lab is successful at introducing how to use the equipment, but this is the only time all semester that we will use the oscilloscopes. That being the case, I’m not sure whether it’s worth introducing oscilloscopes in our class. I don’t know how much our introduction helps a student whose next exposure to an oscilloscope is a semester or a year later.
This is the first semester that I gave the mechanical waves survey and it’s the first semester that I’m trying to incorporate some of the UW tutorials, so I’m trying to figure out pacing. I’m going to delay introducing sound waves and move into standing waves on a string next week so that we are prepared for next week’s lab. I’ll introduce sound waves and their representation in terms of pressure deviation vs. average particle displacement the following week along with standing sound waves. I think this will keep us on pace OK but I do feel like there is less breathing room in this unit compared to last semester.
Brain dump of what happened in the first week of this semester.
Started the first day by giving students 10 minutes to brainstorm in groups and come up with a list of topics they would like to discuss this semester. Their lists contained a variety of topics but by far the most common topic was aliens. This is fine by me. Aliens and habitable zones will provide a motivation and theme around which to organize our discussions of planetary characteristics, life cycles of stars, searches for exoplanets, and the scale of the universe (which I told them during the second day of class). After their brainstorming, I talked a little bit about how I want the class to work (discussions, tutorials, building on intuitive ideas). The first day finished with an administration of the Astronomy Diagnostic Test which took 25-30 minutes.
The second class period we defined some terms related to the Celestial Sphere and students worked in groups on the first Astronomy Lecture Tutorial. After the tutorial, we went through some clicker questions to check their understanding and I assigned the second lecture tutorial for homework.
We built cardboard sundials for our first lab. I wrote some pre-lab questions asking students sketch the sun’s approximate position and sketch a tree’s shadow at different times during the day, but we didn’t pause to discuss these so it’s hard to say how effective they were at cueing relevant intuitive ideas. Every student made his/her own sundial so there was varying levels of discussion and collaboration between groups. We spent the first 1.5 hours inside working through the activity handout and measuring and cutting the cardboard. The last 20 minutes we went outside so students could practice how to use their sundials. It was VERY hot and 20 minutes was almost too long to be outside. I told students they needed to sketch their sundial base showing the gnomon’s shadow and that I had to initial their sketch before they could leave. I think this is a good idea, but many students made very poor sketches showing little to no information and I didn’t do a good job of asking to see everyone’s sundial in action along with the sketch so some students may have copied from a classmate rather than testing their own sundial.
At least two-thirds of my Physics 2 class had me for Physics 1 last Spring so I didn’t feel the need to spend a lot of time talking about class format. Instead, I set up 5 different experiments around the room that represent various topics for the semester:
– glow sticks with beakers of hot and cold water
– thermoelectric engine with beakers of hot and cold water
– rare earth magnets and a copper tube
– a Gauss Gun
– battery pack, light bulb and holder, wires, and different types of switches
At the start of class I gave students 25 minutes to experiment with the equipment at their table and to think record their thoughts about the following questions on whiteboards:
– describe what is happening using everyday language
– how might you describe what’s happening in terms of forces?
– how might you describe what’s happening in terms of energy?
– what do you notice that’s interesting?
– what questions do you have?
I was very excited about this idea, but it only went so-so. Students were engaged and generally talkative within their groups, but I had to prod them to get them to record anything on whiteboards and most of their discussions focused on simply describing what’s happening with very little discussion of mechanisms. Unfortunately, I’m realizing that our students don’t get very many opportunities to simply observe a phenomenon and then brainstorm on their own what physics concepts might be relevant for building up a mechanistic explanation. I need to think about how to build these opportunities into class more regularly and what type of scaffolding might be needed. Still, the activity provided an engaging first day and I promised students that we would revisit each experiment throughout the semester as we developed the concepts necessary to explain what was happening. After the initial 25 minutes, I gave students 10 minutes to visit the other experiments and then talked a little bit about class format.
For homework, I gave students an online set of questions about cooking times to answer using their intuition. ‘If your stove takes 4 minutes to raise the temperature of 1 cup of water by 20* C, how long will it take to raise the temperature of 2 cups of water by 20* C?’ etc. I decided to leave the questions as free response rather than multiple choice to try to emphasize that I want them to use intuition and the exact answer isn’t important right now. The next class I summarized their intuitive results and tied each of these back to the equation Q=mcΔT and we used this equation to calculate equilibrium temperatures.
Friday we defined internal discussed some clicker questions aimed at differentiating between temperature and internal energy.
I started the first day by talking about how Physics 3 differs from Physics 1 and 2 (more opportunity for student input regarding topics, more activities in which students uncover ideas on their own, less structured lab activities). To try to get students excited about the course, I showed a video of a Chladni plate experiment and the Mythbusters video ‘Fun With Gases’ and said that these were both topics we would be exploring in our first unit. As evidence that students really do impact the course, I told the students that a year ago we did not have a lab on Chladni plates, but that students were interested and made a compelling case that the topic fit with course goals and so now Chladni plates are part of the class. We finished the first day by taking the Mechanical Waves Conceptual Survey.
As homework, I asked students to complete the first section of a tutorial I wrote to help students apply their understanding of sine and cosine to understanding traveling periodic waves. We spent the next class period working through most of the rest of the tutorial.
The first lab period was our usual exploration of various wave phenomena using Slinkies and sound waves. This is the first time I’ve given the Mechanical Waves survey so students were a little behind where previous classes have been when they did this lab. Students had good patience and when they got stuck trying to get a transverse wave pulse to reflect on the same side of the string as the incident pulse I pointed them to the PhET Waves on a String sim and suggested that they find what works in the sim and then try to reproduce the effect using their Slinkies. (Interestingly, students started out using periodic waves rather than wave pulses when doing superposition and wave speed experiments. I guess the idea of wave pulses in previous semesters came from reading the book ahead of lab and wasn’t necessarily intuitive.) I’m not sure why, but when looking at the phenomena of beats (recording pressure vs. time graphs on the computer) students were more explicit this semester in connecting this phenomena to the idea of superposition they saw with the Slinkies.
We were talking about special relativity tonight in Physics 3 and we had a good discussion about relativistic mass. I wrote the expression m = m_0/Sqrt(1-v^2/c^2) and gave a hand waving argument for why we say that mass changes with velocity. A student then asked if mass *really* changes or if it’s just something we say to make the math work. Is there an experiment that if conducted aboard a spaceship and viewed from a different inertial frame would lead the viewer to conclude that mass had increased?
Relativity isn’t my strongest area and I didn’t know the answer so I started thinking aloud ruling out the first few potential experiments that came to my mind. A student looked like he had an idea so I passed the question to him and from there we had a great discussion with multiple people building on and refining each others’ ideas to try to come up with an answer. It was great and I enjoyed being a discussion participant on equal footing with the students.
On the drive home, I happily thought about how this was a good interaction where we were legitimately doing real science – proposing and refining ideas, trying to understand each others’ ideas, using analogies and counterarguments, etc. We’ve had a couple moments like this in Physics 3 and reflecting on them I realized that they all sprung from students asking a question to which I did not know the answer.
This leads me to ponder two possibilities:
1. Are there lots of other instances of real science occurring, but I don’t notice them as easily because they don’t involve *me* using the tools of science to answer a question that is brand new *to me*? Are there instances in which student-to-student discussions represent real science interactions but they don’t jump out at me as much because they are questions and interactions that I’ve seen before?
2. Do I inadvertently suppress moments of real science when I do know the answer? Do I answer too many questions or somehow indicate to the class that I know the answer and thus remove some of their motivation to contribute to constructing an answer?
It would be interesting to gather a collection of real science moments from the following categories: 1) student-to-student w/o instructor contributing, 2) student-to-student-to-instructor with instructor contributing when I do know the answer, 3) student-to-student-to-instructor with instructor contributing when I do not know the answer. Would there be differences in the genesis of the moments? In how students perceive the moments? In how/when students contribute to the moments?
Overall I think the Intro to Waves unit in Physics 3 went smoother this semester than last. Quick recap…
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.
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.
I asked the following question when discussing 2D kinematics in Physics 1 this semester:
A ball is kicked with an initial speed of 32 m/s at an angle 40o above the horizontal.
a) What are the x and y components of the ball’s velocity 1 second and 3 seconds after being kicked?
b) How high will the ball go?
c) 60 m in front of where the ball is kicked is a 12 m tall wall. Will the ball make it over the wall?
d) For the same initial angle, what is the minimum initial speed required for the ball to make it over the wall?
Ignore the fact that 32 m/s is somewhat unrealistic as a speed for a kicked ball. What makes part d) more difficult than part c)? Take a moment to answer to yourself.
My initial thought when writing this question was that parts d) and c) differed primarily in their algebraic complexity. In part d), students need to solve for time in terms of v0 and then plug that algebraic expression for time into a second equation for vertical position. I was wrong. The algebra is nothing compared to the difference in how vector components need to be conceptualized.
In part c), students are given numerical values for v0 and theta and they can use v0*cos(theta) and v0*sin(theta) to calculate x and y components of the initial velocity. A student can successfully complete part c) thinking of v0*cos(theta) and v0*sin(theta) as nothing more than algorithms. A student who thinks of these expressions as procedures for computing x and y components with no physical meaning on their own can be successful on part c).
In part d), a student must recognize v0*cos(theta) and v0*sin(theta) as entities that have physical meanings in and of themselves. By this I mean that a student who knows to use v0*cos(theta) to calculate v0,x does not necessarily know that v0*cos(theta) can be used in equations in place of v0,x. In order to solve part d), a student must see v0*cos(theta) and v0*sin(theta) as entities rather than just procedures. These expressions need to be seen as every bit as physical as v0,x and v0,y.
This point was driven home to me when a student who had solved part c) asked for help on part d). I said (unhelpfully) that you follow the same process as for part c). The student wrote 60=v0,x*t and said ‘but I don’t know vo,x‘. I asked if the student could relate v0,x to the initial speed and the angle and he wrote v0,x=v0*cos(theta). I then pointed at this expression and said that we want to replace vo,x in his first equation with v0*cos(theta) because then we can solve for t in terms of v0. The student’s response was, ‘Oh, I didn’t realize we could use this (v0*cos(theta)) to, like, represent the x velocity.’ What an eye opener for me as an instructor!
This is a nice example of something Sfard calls reification. The Closes introduced me to Sfard and reification a while back, but I need to have another read and think about the implication for vector components.