The Physics of Musical Scales

This is a two-for-one post: 1) I saw a great article in the American Journal of Physics that relates to a 2) musical instrument building project I do with students.

The Article

Check out this interesting-for-the-classroom article in the October issue of American Journal of Physics called The physics of musical scales: Theory and experiment. The authors not only teach the reader all about different musical scales but they also have written a free, open source MIDI tool to explore these scales.

I’ve just started playing with Temperament Studio. Thankfully, the authors have helpfully included a button in the software labeled “Things to Try” as I’m pretty much non-musical.

Temperament Studio is free.

Temperament Studio is free.

What if? for my class

We’ve built musical instruments the past few years in my classes. And because it’s often the first big building project many of my students have undertaken, there are always snags with some kids. Most notably are two: lack of any prior experience with hand tools and no tools at home.

What if I invite one group per class to do something with this paper? The pair could study the paper and teach everyone else about scales, demonstrating using the software described in the paper — instead of building an instrument. I think we’d all come out of it knowing more about music.

Instrument presentations

Yesterday, my classes all presented their musical instruments. These kids have built everything from pan pipes to thumb pianos to guitars.

A few innovations to the presentations this year kept it interesting and fun:

  • we did presentations circle time-style, meaning from a seated position on the floor
  • every group played their scale, played enough of a song for us to guess at the title, and talked about something interesting from the building process
  • they have the time over the weekend to put a data section and photos of the finished instrument into the research paper they submitted previously

And that’s another year on the books with the musical instrument project!

Return of the 180 Blog

Screen Shot 2015-08-15 at 10.32.04 AMMy school year starts on Monday and I’m excited to bring the 180 blog back.

Last year, I fell prey to getting too busy to keep up with the habit so I figured out a solution I love over the summer school semester: take a picture, share it to Instagram tagged with #180blog, and let IFTTT send it over to WordPress. I wrote about the details in IFTTT Improves my Daily Blogging Habit.

Below are my top 3 favorite images from the last 12 months:

Day 49: Pneumatics Test Board

The students built this board to demonstrate how pneumatics work as part of our robotics team’s student-led training module. More than the picture or even the lesson, I’m most proud of the camaraderie among the kids who built the board.

Day 63: Can you light a bulb using a battery, one wire, and a bulb? Sketch your attempts.

This lesson is how I open electric circuits every year.

Day 55: Using candles when you run out of optics bench supplies

When I ran out of working light bulbs, two groups got candles. This flickering flame is the second coolest image ever captured on an index card — the tree outside our window wins every year.

Parent Letter 2015-16

Hey there friends! I need advice from y’all: What would you say to parents in an introductory letter? My students are high school freshmen.

My pain: I won’t meet parents until Parent Rotation Night in September (about three weeks into school) at which time I get 10 minutes with an entire class’ set of parents. I’m supposed to give them a taste of class, not explain how I assign homework (etc, etc).

My solution: I’ll email a letter to the parents of all my students explaining how class works. I need to edit this down for length and am not convinced I’ve said everything that’s important.

Dear Parents,

Hello! I’m Megan Hayes-Golding and I’ll be teaching physics to your teenager this year. This letter will explain how class will work and answer the most frequently asked questions I hear in August.

About Me

This is my fourth year at [school] and I’ve taught college prep physics the entire time. In addition, I also help coach the robotics team, am a part-time outdoor ed faculty member, and I help sponsor the LGBTQA student affinity group. Before [school], I taught math and physics at [old school] High School in [other] County. Overall, this is my 12th year teaching.

My educational and professional background is in engineering and as such, I had a short career in industry before teaching, working for two Atlanta companies. The first was DVT, an engineering firm that made machine vision systems to perform quality control on manufacturing lines. After that, I worked at SecureWorks, an internet security service provider. Both gave me rich examples I draw on in class on a regular basis.

I’m highly active in several professional communities online. I blog and connect over Twitter with math and physics teachers around the world. For a peek into our classroom on a daily basis, I encourage you to check out, which is written for other teachers as a forum for me to share ideas from my classroom.

The kids usually identify me by two things before they even know me: 1) I’m the one who rides the purple motorcycle in the parking lot and 2) I like comic book superheroes.


My teaching philosophy can be summed up as “everyone can find something to love in learning physics.”

Everything we do is scaffolded so that each assignment ramps up the personal responsibility and the stakes. Allow me a few bullets to explain:

  • Labs: These collaborative events in class give students a chance to play around with their developing understanding of new material. Throughout the lab, students field my questions and adjust their write-ups accordingly. This is a low-stakes environment where students are encouraged to talk about their thinking. Perhaps you remember labs from your own school experience. Our labs are probably more open-ended where yours were more scripted. We are looking to develop an intuitive understanding of physics in the lab.
  • Homework: I give students multiple attempts at the online, graded homework assignments. Though homework accounts for only 5% of a student’s semester average, I’ve found a direct correlation between high homework scores and strong understanding of the material (and yes, by extension, high test scores). On average, assignments will take 30 minutes to 1.5 hours to complete. There is usually one homework assignment per week, which I encourage students to complete a little at a time. I encourage students to work together on homework. No two students have exactly the same set of questions, which encourages them to discuss big ideas rather than memorize a series of steps.
  • Quizzes: Like homework, students can retake quizzes. I count only the best score they achieve so there’s great incentive to keep working until the concept is mastered. My retake quizzes are different than the first attempt, so I can be relatively certain the student isn’t simply memorizing a set of answers. One layer of scaffolding drops away at this level – students complete quizzes independently while consulting their open notes.
  • Tests: Every unit has a final test at the end. Students may consult a formula sheet they’ve prepared for the event. The final layer of scaffolding that falls away here is that a test is a one-chance-only event. No retakes.

I’m including a copy of the syllabus your teenager received on the first day of class. You’ll see that we begin with a study of Sound Waves. In this unit, the students have a major project to build a musical instrument to demonstrate their understanding of the physics of musical instruments. This project will be due around the middle of September. As it’s the first big project in the class, many kids will surprise their parents the night before it’s due asking for a last-minute Home Depot run. Don’t be fooled! They’ll receive the details and due dates for the project the first week of school, so have plenty of time to ask nicely for that trip to the hardware store.

Getting in Touch

You’ll be at the Parent Rotation Night on September 8, right? I definitely look forward to meeting you then and giving you an in-person taste of how physics class runs. Additionally, I’m happy to field your questions through my school email address, [email redacted].

I encourage you to put the responsibility of approaching me about grades and assignments on your kid, though.


It’s going to be a great year!


Megan Hayes-Golding

Physics Teacher

Camp Megan: The Diddley Bow


Today, four girls from grades 4 through 8 and I built a diddley bow as described in this video:

I picked this project because I wanted to test build a string instrument possibly for use in the fall with my freshmen in physics class. For that, I’m looking to get build time under an hour for a class or 20 kids. This was definitely more than an hour so I immediately looked into ways to speed things up and take the risk of power tools down a few notches.

Materials & Tools

Your diddley bow will consume the following materials:

  • 1″ diameter dowel, $4
  • Cigar box (cardboard preferred and as large as you can find), free
  • Hex bolt 5/16″ x 3/4″ and matching nut, $0.15
  • Hose clamp for 1″ diameter, $1
  • Guitar string, $2 (est)

And use the following tools:

  • miter saw
  • belt sander
  • Power drill
  • Assorted drill bits
  • 1″ spade bit (to match your dowel diameter)
  • Hole saw bit
  • Philips & Flat head screwdrivers
  • metal files/rasps or sand paper

Comments on Building

I recommend cutting your neck to 2 to 3 feet long. In a classroom setting, unfortunately, each kid would need their own dowel, about $4 each. If I were to build diddley bows in class, I’d cut and sand the necks in advance to save time.

When drilling the holes in the cigar box for the neck pass through, offset these holes toward the front side of the cigar box. Ideally, the neck will pass just beneath the front as shown here:


Drilling the neck holes also took us a long time today. In a class of up to 20 kids, I don’t see how I could supervise every kid drilling two holes in a cigar box. I’ve posted a possible solution below under Next Steps: a rectangular neck.

When you go to attach the string at the bottom of the neck, I recommend adding a grommet so the string doesn’t tear up or out of the neck. I couldn’t find any pop rivets with the center knocked out, so we skipped this part. I can see that our strings have enough tension they’ll eventually pull out. I need to think on how to improve this part of the diddley bow’s design.

I didn’t struggle with it but several girls had trouble attaching the string to the screw at the top of the neck. Putting enough — but not too much — tension on the string before tightening the screw down was tough. That’s why below under Next Steps I’ve noted that I want to figure out some form of a tuning peg.


Based on watching other diddley bow demonstrations on YouTube, I’m pretty sure my string could use more tension. I know that was the fact with several of the girls’ instruments.

Next Steps

  • Try going with a rectangular neck like this guy did with a broken hockey stick. This could eliminate the power drill step of drilling out the neck holes on the cigar box, to be replaced with cutting out a rectangle with a box cutter.
  • Replace the pop rivet grommet at the base of the neck with something more readily available.
  • Get a tuning peg at the top instead of just a screw. I hope to find a DIY peg idea.
  • Play with a pick and a slide — can I make or substitute common materials so I don’t have to buy?

Class Applications

If I go forward with this class assignment idea, I imagine building the same diddley bow with all the kids then getting them to mark off the neck for a complete octave of notes. Alternately, the video at the top of this post has some instructions in it for marking off a series of notes for common blues progression. I could ask the kids to calculate why the ratios in the video work.

The current musical instrument project is wide open: build an instrument and explain how it works. Some kids feel this is too wide open for them. Perhaps we can learn more physics if we build a common instrument and study it in depth.

About Camp Megan

This is a thinly veiled opportunity for me to observe how kids younger than those in my classes handle building a project. It’s sort of physics projects beta testing. My brother named it “Camp Megan” and would like to see me turn this into a real camp instead of just beta testing physics class projects. Meh, maybe, that’s a lot of work.

Check out the first Camp Megan: Catapult Build from earlier this summer.

What If Momentum? Game

I want to expand on something I mentioned this afternoon over on my 180 blog — the What If Momentum? game I kind of accidentally created.

Data Collection

Start with the Collision Lab PhET simulation.

Get the kids to collect data about momentum in different scenarios. I used Wendy Adams’ contributed lesson to guide them. Watch carefully what the kids are doing then snap a few screenshots of scenarios you know they haven’t tested. Let them work through all the scenarios before moving on — I asked them to look at collisions between identical masses, different masses, and inelastic collisions.

Here are the data my kids collected today:

Screen Shot 2015-07-09 at 5.55.42 PM

I told the kids I didn’t have a preference on how or where they collected data so they agreed on this Google Spreadsheet. I also refused to guide them on how to set it up (except in one case: they weren’t sure how to best organize the initial and final data, so I made two suggestions and they chose one).

What If?

Here’s the game part.

After about 30 minutes, tell the kids, “Good, ready? I’m going to show you a few scenarios you’ve never seen before. You have to reason through them with your lab group. Together, answer the questions and provide evidence.”

  1. What is total momentum after the collision?
  2. What is momentum of ball 1 after the collision?
  3. What is momentum of ball 2 after the collision?
  4. What is velocity of ball 1 after the collision?
  5. What is velocity of ball 2 after the collision?

Since I know most of y’all, my blog’s readers, are concrete thinkers just like me, you probably want to see the scenarios we played today:

Ask the class, “What if two objects have a 100% elastic collision? The objects have identical mass and one has twice the velocity of the other. See the diagram on screen.”

Mass 1 is the same as mass 2 and the elasticity is set to 0%.

Mass 1 is the same as mass 2 and the elasticity is set to 0%.

This one was easy for the class. My kids talked about how at the instant of collision, they knew the balls would bounce back off each other and that momentum would be conserved. They reasoned that since total momentum needed to stay the same, the #2 ball would depart the collision having “traded” momenta. I thoroughly enjoyed listening to my one little summer school lab group and hope this scales up well to a full size class.

Here’s the second scenario I showed them:

Mass 2 is twice mass 1 and elasticity is set to 100%.

Mass 2 is twice mass 1 and elasticity is set to 100%.

This one rattled them for a bit. They went down a few dead ends, which they always recovered from because they remembered momentum must be conserved. I was surprised that none of the kids calculated this as if it were a homework problem. Instead, they reasoned through it, eventually giving me answers they were confident in.

Oh, by the way, after the kids gave me their final answer, I pulled up PhET and set up the scenario, got a drumroll, and hit Play. The anticipation in the room was palpable.

Finally, here’s the third scenario I showed them:

Masses are the same and elasticity is set to 100%.

Masses are the same and elasticity is set to 100%.

After all the positive reinforcement from the first two scenarios, the kids tackled this one like pros. It took them awhile but the final answer was spot on. I loved the confidence they had based on their reasoning alone (did I mention no one pulled out pencil and paper to work this out as a problem? though they certainly could have).

Total time to play What If Momentum? was about an hour.  Definitely putting this one in my backpack for the future.

IFTTT Improves My Daily Blogging Habit

I used internet automation service IFTTT to simplify my 180 blogging habit. This post may also give you ideas for other ways to use IFTTT.

The recipe in English

Screen Shot 2015-07-06 at 3.20.16 PMIf I post to Instagram with the hashtag #180blog, grab the photo and post it to my WordPress 180 blog. Do a little formatting in the transition, too.

And in IFTTT

If new photo by megtheteach hashtagged #180blog, then create a photo post on your blog

If new photo by megtheteach hashtagged #180blog, then create a photo post on your blog

Here’s how I created the recipe and the details are below the video.

Trigger (when do you want this recipe to run?):

Tag 180blog

Action (what do you want this recipe to do?):

Create a photo post


Summer School {{CreatedAt}}

Photo URL:



via Instagram {{Url}}<br><br>
Fun fact: this post was created automatically using <a href="">a recipe I programmed on IFTTT</a>. It grabs all my Instagrams hashtagged with #180blog and auto-publishes them.

See the HTML code in this Caption? That’s how I formatted the WordPress post with line breaks and added some text explaining how I set the whole thing up. I’m finding Instagram is easier to use than the WordPress app, plus I like having Instagram get these photos as well.

I didn’t make any settings for Categories or Tags. Post status is set to Publish immediately.

I wish

I need to edit my recipe to also grab video posts as well as photos. Last week, I published a video that didn’t trigger my recipe. Upon re-reading my recipe, I see now that it’ll only trigger after a photo is detected. Even so, it wasn’t a big deal to edit the subsequent post to include a video.

I wish that I had a little more flexibility in titling the WordPress post. Today, I’m using a full timestamp in my title. I’d prefer to edit it down to just the date without the time.

I think the feature request in making is that IFTTT should allow the user to parse some data fields.


The wheels feel off my 180 blog this past January when I was overwhelmed by teaching and robotics coaching duties.

Keeping a 180 blog requires me to do all of the following every day:
1. Take a picture
2. Write a caption
3. Publish picture with caption

This IFTTT recipe helps only with number 3. I have an alarm on my phone to remind me about number 1. I gotta be honest though and tell you that number 3 is sometimes just too much.

Starting in August, my new goal is to publish an uncaptioned photo if that’s the only thing standing in my way to publishing daily.

Thanks, Julie for requesting I write this post!

Camp Megan: Catapult Build

Welcome to Camp Megan, kids! Today’s campers are my niece Maddux and nephew Eli. Since this is our first day, we’re going to start simple by building a small wooden catapult. (Total ulterior motive: this project may show up in my physics classes next year.)

We’re building the Tabletop Troll from Storm the Castle. The provided directions are excellent — the kids and I found it simple to follow along just looking at most pictures.

Gather your materials


A few modifications from the pictured materials: swap wood glue out for hot glue because it bonds faster and swap twine for rubber bands cause I didn’t read the directions well enough.

What tools do we need?

We used a mitre saw, belt sander, and drill press because I have access to them in my school’s workshop. You would be fine with a mitre box and hand saw, a sheet of sandpaper, plus a drill.


Measuring provided a great opportunity to practice multiplication.

Fun math moment: I wasn’t sure I’d purchased enough wood — each kid had two 36″ pieces. Eli and I looked at the plans for the catapult and helped me modify the design to fit it all on the two pieces. In our design, the cross pieces are just 4″ long.


Eli, heading off to 5th grade next year, hesitated over the mitre saw because it’s loud and powerful. I made the first few cuts for him before he was comfortable.

When gluing the pieces together, we had trouble getting right angles, something the kids noticed right away. I used a carpenter’s triangle but it was tough to hold in place next to a hot glue joint. How would you suggest helping kids glue things “right”?


Here are the finished catapults. They take up 12″ x 4″ on the table.

Our original design called for screws, but the smallest I had split the wood, so we ditched them all together. The glue won’t hold up so next time I build these, I need to get tiny screws.

Build time

We spent 2.5 hours on this project.

Eli and Maddux test the catapults

Classroom use

I want to build a projectile motion project out of these catapults. Any readers out there want to share theirs?

My Trip to Maker Faire Bay Area: Saturday at Maker Faire

This is part 3 in a three-part series about my trip to San Francisco to visit Maker Faire Bay Area. I also write about our visit to Lick Wilmerding High School and to the Exploratorium in separate posts.

Maker Faire on Saturday

Attend Maker Faire Bay Area. We arrived half an hour before the gates opened to find hundreds already in line. (Pro tip: get there about an hour before opening time — that first hour we were there was much less crowded than later in the day.)

Highlights included:

  • tintype photography with Bruce Morton
  • Arduino projects that use force, range finding, and other sensors
  • make-and-launch air powered rockets
  • all the light-based exhibits in the dark room
  • a sidewalk chalking spirograph
  • make your own comic book button (a stack of comic books, scissors, and a few button making machines)

My three takeaways were:

  • That chalk spirograph looks like it’d be fun to build. Maybe we could work on this in the design or fabrication modules for the robotics team. Or maybe our forthcoming makers club might want to build one.
  • The build-a-rocket booth engaged a ton of kids while also allowing independent build because they posted good instructions all over the place. This kind of interactivity makes Maker Faire fun for the younger set.
  • I have a lot more learning to do surrounding Arduinos and sensors. My geocache has been in the workshop for about six months and it’s time to finish that off. Next project? Maybe a garden irrigation management system at school.

My Trip to Maker Faire Bay Area: Friday at Exploratorium

This is part 2 in a three-part series about my trip to San Francisco to visit Maker Faire Bay Area. I also write about our visit at Lick Wilmerding High School and Maker Faire Bay Area in separate posts.

Exploratorium Visit

Friday afternoon, we ventured to Pier 15 to visit the Exploratorium. Robin-Lynn, Kristin, and I spent 3.5 hours in this place and only left because they closed.

We played with all the exhibits. Ok, that’s a lie. We missed all sorts of exhibits in our short visit.


We played with light. Kristin teaches graphic design so we talked about how the primary colors of light differ from pigment. This simple shadow demo was fun.

Kristin and I joked around with this illusion of flying. From her POV, the effect could be quite convincing. From mine, it was mostly hilarious.

kristin mirror 2 kristin mirror

Robin-Lynn and Kristin made art at a huge swinging table. We wondered what it would take to recreate back in Atlanta — could it be scaled down?


The last thing we saw was also the best. A replica of a portable tent-based camera obscura:


To give a sense of scale, the door on the right is about 2m tall.


An aperture in the ceiling of the tent must’ve held a mirror to redirect light down onto this white table. Kristin didn’t mess with exposure much on this photo — the door was letting light in AND the obscura’s image was still vibrant.

This Feynman quote on the wall at Exploratorium belongs on our school walls:

I wonder why. I wonder why.

I wonder why I wonder.

I wonder why I wonder why

I wonder why I wonder!

At the Exploratorium, like at Lick, I made note of a few takeaways for my own practice. Here you go:

  • A reminder to always open with the hook, the thing of interest. We saw a gravity-powered calculator that could find square roots and a parabolic mirror that focused heat as well as light. Both would be great demos to show in my own physics classes.
  • We can totally build a tent-based camera obscura in August. Meghan and Kristin say they’re down for the attempt. I think we need to use heavy canvas or something like velvet that’s light-tight.
  • Exploratorium has a ton of free resources online that I need to explore: Geometry Playground, several iPad apps that I could use in the classroom — Sound Uncovered is one, and Snacks — aa way to create classroom versions of the most popular exhibits.

My Trip to Maker Faire Bay Area: Friday at Lick Wilmerding

This is part 1 in a three-part series about my trip to San Francisco to visit Maker Faire Bay Area. I also write about our trip to the Exploratorium and Maker Faire Bay Area in separate posts.


Last week, as we wrapped up classes on the 2014-15 year, my school sent me with two other teachers to Maker Faire Bay Area. The three of us are part of our school’s STEAM professional learning community. Our visit was meant to further our cross-curricular work with this great group of teachers. I liked how the three of us available for the trip were from different departments — it helped me experience all this great stuff through their eyes.

The three of us had tickets to the Faire, plans to visit a high school, and time carved out to see the Exploratorium science museum.

My colleagues are Robin-Lynn Clemmons (math) and Kristin Brown (photography). Here we are on the walk to the Exploratorium on Friday afternoon:


My colleague liked to introduce us as “a mathematician, artist, and a physicist” while we traveled around San Francisco.

Lick Wilmerding High School Visit

When this trip came up as a possibility, I knew I wanted to visit Lick. This school is amazing! It’s over 100 years old and was originally founded as a school of the mechanical arts, meaning it has a strong vocational history. Today, Lick is an independent college prep high school in the heart of San Francisco.

Our host at Lick Wilmerding was Colleen Nyeggen. She teaches physics and engineering classes.

Picture of Colleen and Megan

Another Tweep met in real life!

The first thing you notice when you walk down to Colleen’s classroom is the huge wall of windows she has — looking out over a courtyard of similarly-appointed classrooms. When this part of the school was built, the developers dug out space so that every room would have tons of natural light. Here’s a photo from the upper level. Those double doors in the lower middle of the picture are Colleen’s classroom.

The developers dug down to create what folks call the pit area. The result? Lots of light AND greenspace at an urban school.

We toured the “shop pit” area where all the tech arts classes and her physics classroom are housed. The entire area feels industrial and productive. We observed students working on projects ranging from jewelry, electronics, and woodworking.

shop storage in the table

This is the kind of workspace I envied while visiting Lick — the spaces are airy and incredibly neat. This table holds stock for projects.

Every freshman at Lick takes a course in the tech arts (what you might call shop) called Design & Technology, culminating in a project to build a lamp. Check out the Tech Arts Department page for samples of student work.

Colleen told us that the kids learn to operate all the tools on campus during that D&T course as freshmen. When they come to her engineering class and she wants them to design bridges, they already understand how to both operate the design tools and also how to join wooden parts without glue (see below).


To make space in their curriculum for these wonderful courses, Lick doesn’t offer AP or IB courses. The teachers we spoke with said their students still get into “top” colleges and they don’t see a downside to the decision.

I’d love to build new buildings and design new curriculum based on what we saw at Lick Wilmerding. Of course that isn’t happening, so I tried to distill what I learned at Lick into actionable items for my own practice. Here are those three main ideas:

  1. If you’re gonna do projects, you need storage space for works in progress. The tech arts rooms had plenty of storage space for unfinished work. They used broad shelves and all the vertical space available. Work was kept out of the way and appeared to be un-bothered by students.
  2. A reminder to myself that I shouldn’t simultaneously teach how to fabricate a thing while trying to teach about the physics of that thing (for example, the bridge builders in Colleen’s engineering class already understood designing in wood and cut on a laser cutter before she started with them on bridge engineering).
  3. Service learning offers a purpose to a student’s practice. For instance, the kids built seating and shelving around campus.

I wonder if there’s a way to facilitate school visits — either in person or virtually. Would you like help finding a school you can visit?