A ploty “Heatmap” Tutorial: Starting From Scratch
My nighttime decompression time lately has been used to play with data sets to familiarize myself with some of the functionality of plotly. I’ve worked with a handful of sets of data, but I thought I’d choose one and make a quick tutorial. I am no expert. But if you’re beginning like I am, sometimes you want advice from a novice.
So, here’s a sample plotly exercise I had some fun with. I say it’s been fun, but my idea of fun is orthogonal to the plane . . . And no, physics friends, I do not mean “normal” by that reference!
Obtain a data set from somewhere. Preferably a data set that has meaning to you–or you’ll run the risk of not being motivated enough to produce a great graph (it can take some time). I chose MCAT performance data, since the end of the semester has me thinking of pre-med students and their progress toward their application processes. For a heatmap, you’ll want a typical two variable data set, with some kind of third measure of a magnitude or scalar quantity. I know, that last sentence ended with a redundancy.
Notice the initial score along the y-axis and the change in score along the x-axis. Important for a heatmap, notice the values in the table are along a range, not binary (1’s or 0’s). This is what makes these data a good candidate for generating a heatmap.
This one’s easy. Copy and paste the source/URL somewhere handy. Why not in an extra tab in the same Excel file used to store the data? Put it somewhere, though. Because if you’re like me, soon you’ll have who knows how many browser tabs open and none of them will have the page you snagged the data from. And of course, you’ll have forgotten to bookmark the page. Link to data.
Enter the data into a spreadsheet. For the table above, I entered it in Excel by hand since there wasn’t much data and I couldn’t copy and paste the data from the pdf. It is possible to enter it directly into a plotly “grid,” but I like having a backup copy of the data on my physical hard drive. If you’re lucky, you can just copy the data from the source and paste it in Excel. That’s what I did for many of my data sets, though I often still had to do some transposing. If you find that pasted data in Excel ends up being all crammed into a single cell, try the “Text to Columns…” command pictured below. It just might save you time!
Upload your data to plotly. This is simple, really.
Click on the grid file and hang on! [“Grid” refers to the little four square icon. That’s plotly’s term for “data file.”]
A few quick things right off
- You can share your data table right away if you like by clicking the Share button at the upper right.
- Changing column titles is easy. Just click and type. I found the cursor would flip off the intended header unexpectedly occasionally. Just click on a data cell and then the column header to prevent weird cursor action.
- For some reason, plotly did not like my original column headers -4, -3, -2, . . . +6, +>7. When I tried to plot, strange things happened. That’s why I wrote out “Minus/Plus” for each column.
- plotly may select some columns as x- and y-axes variables for you. Just deselect them by clicking on them if you want to change those.
The heart of plotly, of course, is in the “Make A Plot” function. Click this and (for this tutorial) select Heatmaps
Notice there are lots of options here. It’s easy to switch back and forth. When viewing the grid, just click the Make a Plot function at any time to select a different type of plot.
Play around with which columns to plot along the axes.
- If you’ve been wise in titling your columns, then select “Column Names” for your x-axis.
- I didn’t use the N column. It’s ok to have columns that aren’t plotted. Really. It is. You might do a different plot with the same file later in which you do want to use previously inactive columns.
- The z-axis is what is plotted along a color spectrum emulating “heat” (I hate that term from a pedagogical standpoint, by the way–but that’s another blog entry).
How I did the MCAT plot is below. Your plot, naturally, will be different. So select and deselect away. If the output is undesirable, just close the plot and try different selections.
Touch up your graph with Notes and editing your title, axes. Just click on the existing labels to edit them, it’s really easy.
To add notes, click on the Notes icon. These are created in layers. So to edit them once created, just click on the Notes icon again and select the specific note you’d like to edit from the drop down box.
The + adds a new note. However many times you click the + is how many new annotations will appear on your graph. If you add way too many (like I did initially), then just click the – . Be careful that the annotation you want to be deleted is selected from the drop down box first though. Otherwise you may delete an annotation you didn’t want to (I did this a couple times, too).
Many aesthetic things about the arrow, text and box itself can be edited pretty easily from the Notes icon. And, you can choose to link the annotations to the data or the page. So if an arrow points to a data point of importance, select the link to data. When viewers zoom in and out, the arrow will still point at what you’d intended.
Share your plot! Clicking the blue Share button brings up a box for you to share your plot via email or social media. This is what plotly’s about: sharing data and plots. When plots are shared, those who can see the plots will also have access to the data. However, they will not be able to change your plot (unless you specifically give them that level of access). They can instead, save the data to their own file system and modify the plot as a separate file.
Turn this over to your students! Challenge them to find data of significance to them and then work to represent that data which paints a clear picture of the data’s meaning. I don’t care what discipline you teach–this can be a powerful tool for you and your students.
Data visualization for scientists, journalists and the public.
sharing data for the purpose of data literacy
Disclaimer: This is NOT a tutorial. I’m still learning plotly myself. I’m just writing down thoughts stemming from a recent talk as part of our Title III curriculum re-design grant. For an intro/how-to to get you started, check out Rhett Allain’s December 2013 post here.
I’ve never used the words “mind-blowing” in anything I’ve written before, but it is appropriate for a handful of reasons. There’s so much that was presented and even more that I need to learn . . . So this post is premature as I’m far from an expert. I’m going to try to keep this post focussed, but plotly’s utility and function sprawls like a concept map, so bear with me.
First, the basics
- Create a graph from data. (Duh, right?!) Using data from excel or manual input, a graph is created. Plotly does its best to auto-recognize x- and y- variables. If it gets it wrong, it’s a simple fix, but it’s likely going to get it right, right out of the box.
- Next, fit a function to the data. This is not much more exciting, you can do this in Excel or LoggerPro pretty easily.
- You can edit any feature of the graph and add comments easily through plotly’s GUI. The departures from standalone graphing software begins here. How do you move, modify and embed legends/comment boxes in Excel without skewing the graph, anyway?
- Get creative with how your data are represented. Switching among graph types is a snap and adding a fourth dimension to your data can be done in different ways (datapoint color or size, for example).
- Share your graph and data with someone else privately. Or, share it publicly. The setup is similar to Dropbox, and just as easy. Those you’ve shared your file with will see the graph and the data. You’re essentially sharing the graph’s DNA, not just the final output.
- Graphs can be posted directly to social media outlets as fully interactive objects for others to explore.
So far that’s not really super-wonderful, it’s just a graphing utility that’s gone ‘googledocs-like.’ But wait, there’s more. A whole lot more.
- Others can save your graph with its embedded data for their own work. They can’t change your original file in your account (unless you give them permission to), but they can tweak the settings and output and then save as a file of their own. Then their interpretation can be re-shared. If you are looking for a collaboration, this is great!
- With the notebook feature, changes can be logged. A digital record of each collaborator’s modifications, comments and code all populate a journal for review.
- So next, take your graph and embed it in a blog as an object. Not as a .png or a .jpg, but as a fully interactive object just as it functions in plotly. This enables further sharing among your blog visitors. My attempt at this is below. It’s my first plotly of HS physics teachers in OK per county as a function of county number:
https://plot.ly/~SteveMaier_/3/ok-hs-physics-teachers/ (Unfortunately, embedding plotly graphs is not yet possible in WordPress, but is in github--for for now you'll need to click the link).
But it needs help! Can you save and then edit a version of your own to better represent the data???
“And now it gets crazy . . .” (This is pretty much a quote of Matt’s)
- Plotly will soon have a live feed for users to publish and share their graphs. It has the potential to be the data guru’s version of Twitter. In the future, you may hear someone ask you at a conference “That’s a great representation of the data, have you posted it to your _________ feed yet? I have some ideas of analyses I’d like to explore with you.” My candidates for the blank: plotly, Analytics, graphguru . . .
- If you’ve created graphs in Matlab, R, Julie, Node.js or Python, then you can import them into plotly. Also, use LaTeX for titles, comments or notes on the graph, no worries. Once in plotly, modify any of the features as you like. Then output the entire file in any of the above formats! Plotly is basically the Rosetta Stone of data analysis.
- Plotly now has the capability of converting a static image of a plot into a plotly file. It essentially deconstructs the image of a graph and reverse engineers the image to create a data file. Then the data are used to create a plotly file. This file will have not just the graph, but the data used to create the graph! So take a graph from a periodical or a newspaper, scan it, apply some plotly magic and your students can run analyses on previously published graphs with data comparable to those collected by the authors! Aside from “fact checking,” this could be a great tool for working with data sets that mirror those used by experts in the field.
Some closing thoughts:
To close, I’ll just add some passing thoughts quickly. I really didn’t want this to become a long post, but there are some really neat possibilities here for the classroom:
- Have students import their lab data directly to plotly and share it among their classmates with a class profile within plotly. Lab data could then be crowd-sourced and/or groups’ data could be plotted on top of one another for comparison. This could be informative if each group had a slight variation in apparatus/question.
- If you’re not up to creating a class profile in plotly, just designate a class specific hashtag for quick searches if posts/graphs are in social media.
- Have classes collaborate across institutions! Think about your students sharing data and graphs with high schools a few states away or an ivy league university across the nation.
- What if Vernier or PASCO sensors were used in line with plotly for streaming data off your student’s lab benches?
- A word of caution: my stats committee member would be quick to point out that unless you have formalized your question prior to data collection, then any analyses are purely exploratory. I don’t think plotly minds this. In fact, they want folks exploring, that’s there entire gig. However, broad sweeping conclusions might not be appropriate from data used and analyses completed. This is less of an issue for physical systems.
Take away message: plotly is worth a look!
Well, I caved in and took the plunge!
I recently* purchased an all electric mower.
It is a zero turn riding mower with a 42″ mowing deck.
*Not so recent now. I’ve had it for a few mowing seasons and have 80+ hours logged.
Before taking the plunge, I searched the web for some intel. What I found were skeptical posts dating back to when the mower was introduced (2009?) and a few posts of dissatisfied customers:
The skeptical posts of the unit were by people who did not actually own a Zeon, their arguments were based mostly on the predicted pitfalls of battery life and assumed lack of power due to the power source. Most of the customers’ complaints were corrected, others did not follow up with how their complaints were handled.
So, what I found was intel, technically . . . it was just not very good/detailed intel. Anyway, I decided that if I were to get a Zeon, I’d be sure to make some posts about my experiences.
My lot is about 1.7 acres. There are trees and some sloped areas. The very back of the lot borders a pond with a sandy soil. When I mow, I find that I don’t usually have several hours at a time to mow. More often than not, I can only work for an hour or two before running kids here/there or tending to something inside. So having a unit that can only mow for 60 – 90 minutes at a time fits my needs. Having my own mower, I intend to mow often so the lawn doesn’t get out of control. I doubt my neighbors expect this of me right now due to my mowing history, but I’ve been borrowing a mower from a neighbor and have always tried to limit my use with it. Long story short, I think cutting the grass more often after only slight growth is a good fit for an electric mower (cutting tall grass takes longer and you won’t be able to mow the same area as shorter grass).
My wife and I really don’t want to store a lot of gas or deal with fumes in the garage. Some day I may have an outbuilding. Until then, the mower will need to be in our attached garage. I never like buying 1st generation equipment, especially when very expensive. Being 2013, my expectations are than most of the bugs in the early units have been hashed out.
UPDATE: When I first got the mower, I was playing catch up with overgrown grass. The Zeon does not handle very thick and tall grass as well as a suped up gas mower. It tends to choke out and give an error code a lot if you progress too quickly. What I had to do was raise the deck to its maximum height, trim, then go at it again at a lower height. It was an unfair test for its first use, but I learned its limits pretty early. Once I got into a rhythm, I went along fine.
- The Zeon runs essentially without noise when the blades are not engaged. It really is amazingly quiet. And, it can move pretty fast. It is more than fast enough for me. I’m glad there’s a seatbelt!
- It’s size is small for being a 42″ machine–this has implications I’ll talk about later.
- There are 12 different deck heights settings! These range from 1″ to 4″. If you are clever with the deck safety lever, you can set the deck for an additional height of 4.5″.
- When the blades are engaged, it is NOT noiseless. You don’t need ear muffs, per se, but I recommend them anyway.
- I was impressed with it’s first test: mowing an overgrown side lot (grass was 20+ inches in height). The adjustments for speed were the same as I would’ve had to make with a gas powered mower of equivalent size.
- The Zeon is of welded construction; very solid.
- There’s a tow hole in the back. And it is secure enough to use to pull the unit out of a sandy mess🙂
- This unit is expensive. I gave up an offer on a used 52″ Hustler unit that was 3/4 the price. The reasons: there was a lot of oxidation on the used unit, there was no warranty on a used machine.
- The wheel fenders are plastic–I wish those were metal.
- The fast charger is too expensive. If you want to charge the mower in 6 hours, it’ll cost you $600.
- There is no throttle adjustment like on a gas mower, so there’s no way to limit the max speed when driving/mowing. This is not an issue for me right now . . . but when the day comes I teach my children how to mow, there could be some scary moments.
Notable Points: Experiences So Far
Regarding safety, I know that the roller bar is important. But wow . . . it can be really annoying! I like that it can be folded down, but even that can get in the way. I popped a wheelie a couple times on trees with low branches or others growing at an angle. Lesson learned: a little situational awareness is in order!
When mowing heavy grass, if the motors get choked out, expect error messages on the LCD display. It’s a little disconcerting at first, but Keep Calm and Power Down. Make sure the hand controls are in the parking position and the blades are disengaged before powering back up. If that doesn’t work, while the mower is “on”, move the controls to the drive position, then out to the parking position. Then you’ll likely get the “ready” read-out.
The size of the mower is great! For a 42″ mower, you can get into very tight spaces and do circles around trees like no one’s business. However, what I’ve noticed so far is that my comfort level in dealing with slopes is not as great as the larger framed 42″ gas mower I borrowed up to this point.
Charging takes a while. 21 – 22 hours between uses can be too much to wait for some. I use the down time for trimming and other chores, so it works for me– But this could be a real issue for those with different schedules/mowing cycles.
Motor effectiveness does not decrease as the battery charge goes down. This is crucial! It’s not like a battery operated drill that begins to lose torque or rpm’s due to low battery charge. The motors in the Zeon continue at full pace even when the LCD display indicates only one bar.
To Wrap Up . . .
I’m happy with the machine so far. The lot I’ve been working on was originally 24″ in some spots and very thick. I first mowed at 4.5″. It left a clipping heap with each pass and a line of grass that had to be mowed again. But honestly, at 24″, that’s likely with most any mower. I’ve since gone over some of the lot with the deck set at 2.5″. It handled it just fine; choking out a couple times on the clipping heaps from the day before. My bagger is on order and I’m looking forward to putting it to use!
Resources (links open a new tab)
- Zeon operators manual
- Zeon parts manual
- Smartec guide to error codes
- Hydro-Gear manual for drive system
- Hustler Turf Zeon A post about charging and testing batteries. Last active was 2011.
- Inaccurate Display blog post
- Sensor Location and Available Reference Voltage Technical post about troubleshooting sources of performance issues.
Batteries: The Original Equipment Manufacturer (OEM) batteries are Trojan 31XHS (~$200 a piece), not to be confused with ordinary Group 31 batteries you might find locally. As Christopher points out, there is a significant difference. Something to consider . . . if you are buying a Zeon “new” now, recognize that the batteries may be old. Even if they weren’t ever really used, they’ve been sitting (likely without a healthy charge or water levels maintained). I would recommend getting some assurances from the dealer the batteries are current or have been replaced with factory OEM batteries or an equivalent (compare the specs). Otherwise the life of the batteries may be significantly reduced.
Chargers: Related to batteries, there’ve been some comments about chargers. I still use an OEM charger, simply because my first one failed and I got a replacement for free because it was still under warranty. However, I am really tempted to upgrade to an onboard charger as commented on by Brandon Friesen and Bob Hutchinson. These chargers have four separate leads that can remain attached to the batteries, charging them individually rather than in series like the OEM charger does. This permits the charger to manage each battery independently which cannot be done with an in-line series hookup as in the OEM charger. (The advantage of this is some chargers are capable of reconditioning/prolonging the life of batteries if charging only one at a time). Those mentioned below in the comments include:
- NOCO Genius 4 charger ~$375 on manufacturer’s website
- Minn Kota 440D ~$430 on manufacturer’s website
Another advantage is that some of these kinds of chargers can typically be kept outdoors; even permanently fixed to the mower for convenience. This is not the case with the Hustler OEM charger (see next paragraph).
OEM Charger Must be Indoors: If you think you can get away with putting the charger under the mower tarp while it’s outside charging, you are mistaken. This is a bad idea. The charger needs ventilation and a low humidity environment. It will fail over time if used outside, subjected to daily humidity. I speak on this from experience . . .
Loose Nuts: Check the nuts that hold the deck in place from time to time! I’ve started replacing nuts that have loosened with locking nuts (the dome shaped ones with the plastic inserts).
Day 11 (Monday):
The take-home message today?
Intensity level is a scaled value for sound while sound intensity is more of a raw value for sound (dependant on its frequency and amplitude). And, while intensity can be calculated from physical properties of the source, most references to “intensity” in everyday usage are really referencing “intensity level.”
We worked a problem as an example going back and forth between the two (intensity and intensity level). [If one child is “loud” at 75dB, how loud would a room full of 30 children be?] This activated a standard. So all in all, a productive day. This does lead to a question to others doing SBG: what is the average rate of activating standards? One or two per week? One or more a day?
Day 12 (Wednesday):
We discussed Doppler effect today. For a break in pace, we first discussed how Doppler radar works in an important everyday example (everyone in OK knows about Doppler radar–access to weather data and imaging in this state is phenomenal). Increasing/decreasing distances between reflected wavefronts off of a distance cloud is a concept students grasp well, so I went with it. Then the equation(s) were put up on the board for determining the observed frequency. I like combining the expressions with a +/- in the numerator and a -/+ in the denominator. General rule: choose the upper sign for approaching and the lower sign if motion tends away from the other. We worked a couple of examples, then I gave a more challenging/conceptual question:
If you are swinging a buzzer at the end of a string in a circle with a constant angular velocity, what would the observed shifte frequency as a function of time plot look like?
To force students to consider a scale on the plot, I gave values for the angular velocity, radius of the circle and the frequency of the source. A curious feature of this problem is an unexpected hangup students had (and I should have anticipated it): confusing the angular frequency = 2 f of the swinging sound source with the frequency f of the sound coming from the source.
Anyway, long story short: after all was said and done, all of the standards were active at the end of class. I’m getting excited about moving on to new material–now I just have to polish up the new standards!
Day 13 (Friday):
Pop quiz again! This time we looked at a video: http://www.youtube.com/watch?v=_d8ROhH3_vs . The question was,
For which segments of the film loop are depictions of the Doppler effect accurate and innacurate?
I’d intended this to be a real quiz, but we ended up talking about it as a group discussion. It turns out students could answer it pretty easily, but even they recognized that they’d never really questioned sound effects like this before.
Day 7 (Monday):
We closed out Chapter 15, activating the last remaining standard. In hindsight, there were some “neat” things we didn’t do in this chapter (derivations and a few extra demos). But in the interest of time and really trying to focus on the standards, they simply didn’t make the cut.
I also haven’t given a pop quiz yet. That will happen next class, maybe. As the time I thought was right for a pop quiz today, we ended up using it as a mock assessment. I drew two wave plots on the SmartBoard and asked them to write the corresponding wave function. They were also supposed to include values for amplitude, period, wavelength, wave number and periodic wave. After going over the answers (which were on small whiteboards), it was clear no one would have gotten a “3” or a “4.” Students agreed that the scores earned would have been a “2” or “2-ish.”
Day 8 (Tuesday):
Today (in lab) we pulled from Chapter 15 a bit to serve as an introduction to sound traveling in an air column. While a string under tension is different from sound, the expressions for the normal modes are the same for strings under tension and sound if both ends of the sound column are open or closed. So I started by drawing diagrams of the standing waves for both ends closed (string and sound); noting nodes at closed ends, antinodes at open ends. We derived the expressions for the normal modes and showed they were equivalent. Then, a series of diagrams of sound tubes with one end open, one end closed revealed we’d need a different expression where n = 1, 3, 5, . . . applies, rather than n = 1, 2, 3, . . .
And <pouf!> Standard 16.4 (a lab standard) became active.
To demonstrate how sound consists of a source undergoing vibrations, I showed the second half of this YouTube video: http://www.youtube.com/watch?v=C5LS6scAL3E It’s worth watching, and it has a little bonus at the end about filming rate. I wish the narrator made reference to beat frequencies as an analogy to what is being observed (f_ beat = f_tuning fork – f_filming rate|).
Anyway, the task for students in this lab was to determine the speed of sound empirically given two tuning forks of known frequencies and the apparatus below:
Jokes and confusion ensued as everyone fumbled around with how the 2nd normal mode is the 3rd harmonic and the 5th harmonic is the 3rd normal mode, etc. Kind of a “Who’s on 1st” banter.
A student mentioned having seen a video of a series of pendula showing neat normal modes. I knew just the video he was talking about: http://www.youtube.com/watch?v=yVkdfJ9PkRQ I made the comment that constructing a demonstration like this (having determined string lengths and normal modes ahead of time) would get a 4/4 on one or more standards🙂
Day 9 (Wednesday):
Well, I forgot the pop quiz. Again. Good thing these posts aren’t published until the week is over! Pop quiz to be given on Friday, maybe🙂
Spent time today on wave interference. Having two large tuning forks attached to wooden rectangular boxes (with one end open) really helps demonstrate how one wave can drive another. Adding a movable mass to one of the tuning forks illustrates beat frequencies well, too. One student brought up tuning instruments in band, trying to hear the beats everyone was talking about. A perfect example from previous experience to tie in to class!
Discussion of Bose sound systems, noise cancellation features of automobiles and noise cancellation headphones led us to working a problem involving two speakers creating interference for an observer some off-center distance away. Having reasoned out the relationship ahead of time, we found a typo in the textbook’s example. (f = nv/d where n = 1, 2, 3, . . . for constructive interference; f = nv/2d where n = 1, 3, 5, . . . for destructive interference).
While it wasn’t announced today in class, this essentially activates Standard 16.2. I’ll have to announce it officially in Friday’s class.
So is it ok to activate standards out of sequence? I think the answer is yes–at least that’s what’s happening this semester and the flow of the course doesn’t feel weird, anyway.
It just seems natural to talk about beat frequencies immediately after addressing and working with normal modes of waves. We’ll get to intensity and intensity levels soon enough, just not in the order Young & Freedman have it printed in the text.
Question: I know that you can sustain hearing damage if subjected to intense sound, even if out of the audible range. However, if you are wearing noise cancellation headphones and there is a very loud sound they are cancelling out by producing waves that interfere destructively, are your ears more susceptible to damage by receiving a pair of out of phase sound waves? Or, does the cancellation really mean a decrease in vibrations received by the ear?
Day 10 (Friday):
Well finally, Friday arrived and I remembered to give the pop quiz! The problem was given at the board. No numerical values:
You walk in front of a concert stage with two speakers at either end (separated by a distance L). As you walk from in front of one speaker to in front of the other speaker (parallel to the stage), plot the volume of sound you would hear as a function of L. Assume the speakers are emitting a constant tone of the same frequency.
I’d secretly planned to ask a student to come to the board — just hoping for a 3 or a 4 performance for our first standard. And we got it! By the end, we were all chiming in. And the diagrams drawn by the student were pretty thorough, addressing:
- Interference patterns if the tone emitted were perfect and no other interference/reflections were occurring
- Interference patterns if the speakers were playing music with multiple tones
- Correct scale in terms of L as to where minima and maxima would occur
- What the idealized interference patterns would look like if the frequency of the tone were increased
There are a couple of points I’d like to make as to why today’s class made an impression on me and my students:
- At the beginning of class, someone said “No one likes pop quizzes” <shaking head with a quiet groan>. However, it soon became clear that quizzes are (in this class) an opportunity to submit a standard. And hey, if you don’t do so great, then you can learn from it and resubmit. The pressure to perform was alleviated.
- If someone is absent from class and misses the quiz, that just means they’ll just need to submit that standard on their own. Students will likely share what they did in class during the absence
Anyway, I had to leave campus early in the afternoon, so I wasn’t able to get a screen capture of what was done in class to post and share. But that’s what I wanted to do, to brag about how the discussion went and how well questions were fielded; all of which is the subjective litmus test for assigning it a 4/4 (per Andy Rundquist!).
Most of this entry is just journalling. SBG stuff can be found toward the end.
Day 5 (Tuesday): Clothesline Lab
(Monday was MLK Day)
The short of it: what we did in lab today addresses Standards 15.2, 15.4 and 15.5. Not in entirety, but quite a bit of each.
Lab began with me drawing a picture of a standing wave on a string on the board (y vs. x). I had the students tell me what the measurable quantitites were. Amplitude, wavelength, # of nodes and one student even got at linear density of the string. I was impressed! Replacing one end of the system with a pulley, it became obvious tension in the string was an additional variable that could be measured.
I have to admit, I did some handwaving about how the velocity of a wave on a string is dependent on tension and linear string density. But knowing the derivations is not really an important part of the standards. It’s an example of how really neat derivations can be good exercises, but not critial for understanding the course content as a whole. This SBG approach is really pressing me to trim the extras so we stay on task.
Following a brief introduction of waves on a string, students were introduced to the CENCO string vibrator. They were then tasked with collecting enough data to write out a wave function
y(x, t) = Acos(kx – ωt).
The catch: the frequency of the string vibrator had to be determined from a plot of wave velocity versus wavelength (the slope yields frequency).
Application exercises included writing out y(x, t) for x = 0 (pretty straight-forward) and confirming whether or not the location of the nodes are consistent with their wave function (not so straigth-forward, since x = 0 is problematic). I hope my students recognize that since the system is symmetrical, they can measure x from the node at the pulley rather than estimating it from the tab.
Day 6 (Friday):
Announced that the lab standards (there were 2 of them) were now active. This was after a discussion of lab and average power of a wave on a string. I did not spend much time on the derivation of the equation, but did refer back to the relationship of power in terms of force and velocity. From there,
P = F v
P = F(x, t) v(x, t)
I made loose reference about how there were steps involving calculus lingered in arriving at F(x, t) and v(x, t). I don’t like handwaving explanations, but the steps are outlined pretty clearly in the text. Instead, we used data collected from lab to investigate something I’d noticed “kind of” in the past, but became more clearly defined in Tuesday’s lab.
Students noticed that the amplitude of standing waves on a string varied: the greater the tension, the greater the amplitude. It wasn’t huge, but enough to be noticed. So, we calculated the wave number and periodic wave for four separate standing waves. We then calculated the power associated with each and plotted power as a function of tension (for a stretched wave on a string). I was honest with students and told them I’d never plotted this before, so wasn’t sure what to expect (linear vs. non-linear trend). It turned out to be fairly linear, however a third order polynomial seemed to fit it pretty nicely too. But with only four data points, we decided we’d like to see this done for more data plots. . . maybe one of them will take the initiative (hint, hint!).
The good news is, all of this was directly related to the lab standards. Solving problems involving the normal modes of a string under tension and the wave’s average power. On a side note, I am really looking forward to weeks where there aren’t interruptions in the class week (days off, sickness, etc.)–the next few should be pretty solid weeks.
Students commented that they were excited about SBG. They thought the work load was going to be more at first. However, once they started understanding the material and fully reading the standards, they saw how the standards could be address with a thorough problem. In each of my standards and recommended assignments, I list a “The Point” sentence. In this statement I come clean about why I’m asking them to do that standard. In part this is an open way of being accountable for what I assign and justifies the work (no, it’s not just “busywork”), but it’s also a pretty overt way of being transparent with students. This works well with my calc-based physics students since they are engineers and like to see the applications/worth of things. I don’t know if students in other classes would appreciate it as much.
Day 1 (Monday): Syllabus review and Screencastomatic
In all fairness, I hinted to my students at the end of last semester that there were changes coming this spring, so they new something was up. Still, I thought things went pretty well. They liked the idea of always being able to improve their scores on the standards. There was some interest/concern over the screencasts and the ways that standards could be submitted. As this is the first go of things, I have to admit I’m interested to see how it is all going to work out, too. I anticipate questions as soon as the first standards become active.
Demonstrating how Screencastomatic works seemed to help the mood of things. Students were more at ease knowing that this application ran without requiring an install. Plus, our lab has a SmartBoard and I told my students they could use it if they wish.
I emphasized my reasons for the shift to SBG (previous post) and that since was new to all of us, I’d be seeking their thoughts on it throughout the semester.
Day 2 (Tuesday): Notes and demos instead of lab
Because Day 1 was consumed with syllabus, SBG discussion and a screencasting tutorial, today in lab we forged ahead with notes and demos. Also, I have a meeting in OKC on Wednesday, so notes during the first lab was an intentional preemptive strike to stay on target. By the end of things, standards 15.1 and 15.2 became active. Class ran pretty smoothly. I found myself referring to my list of standards more than my notes/text.
Class/lab began by collecting data with a Vernier sensor and looking at a y-position time plot of a hanging mass. We were able to get a sense of what simple harmonic motion “is” (tough those words were not used). Discussion of the data led to identifying what physical properties could (and could not) be determined from that kind of plot. Then we looked at the Columbia Wave Machine (ca 1908, sporting its infamous “ether” waves!).
Also demonstrated the Air-Zooka. I leveled with students and told them that I used to think it generated solitons, but am now pretty convinced its just a wave pulse. If any of you readers have input on that tidbit, I’d appreciate it!
At the end of class, two students visited with me for a while about SBG. Overall, they are interested in the concept. One is even excited at the idea. Though they are not convinced I’ll be able to keep up with all of the standards and the active times per student across all standards for the entire semester. Can’t say as I blame them–I’m really going to have to be a better accountant of dates, due dates, assignments, etc. The suggestion came up that the number of resubmits be limited to three times or so.
At the beginning of the class, I visited with students about this blog. I asked for their permission to write about our experiences as a class. They were ok with it, so it looks like I’ll give it a shot. So long as I don’t get to swamped with things (or too wordy with posts!), I’m going to try to continue this open journal for the duration of the semester. Last year my physics road signs got off to a great start but then died off. I could have said it came to a Dead End, but that would have been a pretty lame joke . . .
Day 3 (Wednesday): No class, students to brainstorm about their semester projects
Day 4 (Friday): Example problems and SHM wrap-up discussion
Discussed the differences between systems that are periodic and those that exhibit SHM. Also discussed damped vs. driven systems. Most of this was conceptual. A question of the standards came up: can examples used in class be submitted for standards. Short answer: No. Some background . . . one of the standards requires students to provide two examples of systems exhibiting SHM and two other examples of systems that are periodic, but do not exhibit SHM. We talked about pendula, the infamous cat clock pendulum, a bouncing ball and a PASCO cart “bouncing” back and forth on a track.
Consider a system that is imaged by an open camera frame and a strobe light. How would the object be imaged on the film? Would this be representative of a Hooke’s law type force? (x, v, a as functions of t)
We derived the velocity and acceleration expressions for the general wave function. No big deal, just two derivatives. The representation: a (x, t) = -Aω² y(x, t) took students a moment to assimilate.
I feel as though I could have armed them more for tackling a standard. “Discussing” and talking about plots of these functions is different from having them generate/look at real data themselves and function fit. Classes earlier in the week were more meaningful than today’s, I thought. With no class Monday due to holiday, we will have to spend lab on Tuesday looking at wave functions so they can see applications of this stuff. Wave function for a vibrating string under tension???