Standards Based Grading, Week 3
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!).