Day 13 - String Tension

The Problem...

How much force is there on the neck of a guitar?

Why?

• Illustrate relationships between science, math and music
• Students learn to research and collect experimental data in a procedural way
• Connect the Forces unit to the Waves and Sound Unit of Grade 11 Physics

This is an activity I have done with some of my more science-inclined guitar students.  I simplified the problem for them however because I didn't want to take up too much lesson time.  We collected the data over several lessons and I put it in a spreadsheet that tallied the values and gave an answer for all the strings.  The sheet I gave my students looked like this:

In a Science Class...

If I was using this in a classroom, I would let the students come up with ways they could find out the tension in the strings.  I would give each group of students a different stringed instrument (based on what I had available or the music department would be able to provide): guitar, ukelele, bass guitar, mandolin, banjo etc.  Student's could even bring in their own instruments to analyze.  

First, I would have students write down an estimate of what they think the total tension would be.  Again, in problems such as these, its always a good idea to have some idea of what the answer will be before actually calculating it.

They would then work Collaboratively to figure out how they are going to measure the tension.  It's hard to measure string tension directly when the string is on an instrument but there are ways to indirectly find it (see picture above).  If they discover that formula, they will have to think about how are they going to collect data on:

• the length of the string - can be directly measured
• the fundamental pitch of the string - there are many free mobile device apps that will tell you the pitch of a string
• the unit weight of the string (kg/m) - could use the diameter of the string and the density of the string material.  Alternatively, could put a length of string on a scale.
• the diameter of the string - can be directly measured using callipers (diameters also tend to appear on string packages)
• the density of the string material - most likely this would be looked up on the internet

For some of the variables, internet research will suffice and for others, they will need to measure themselves.  They will have to decide themselves what is appropriate for their situation.

Alternatively, they may start by looking at a package of strings, which usually lists the tensions on the back of the pack.  But then they have to think about what they are presented with and read the fine print.  What assumptions are made?  Do those assumptions apply to their instrument?  Probably not.  Also, they may not actually know exactly what brand of strings are on the instrument.

Let them decide...

An important part of Knowledge Construction is to let the students decide how they are going to meet the success criteria.  Although some groups may end up doing more work than others, all groups can present their results back to the class so (hopefully) a variety of creative and innovative ways to measure the tension are covered.

Apply it...

Now that students would have an understanding of how string pitch, length, diameter and density are related, they could apply it by creating their own string instruments.  This could be turned into an interdisciplinary project between science and music or art.  They would have to answer some of the following questions (and more) before starting to build.

• How many strings?
• Will it have frets and will it be based on the Western 12-Tone Equal-Temperament scale like a guitar or a piano?
• What material will the strings be?
• How strong will the support of the strings have to be? (ie. what would the tension in the strings be)

Extend...

This is a cool video that I think would be good for a follow-up on exactly what a string does when it is plucked.  How come they look like that in the video?  Do they see that when they regularly pluck a string?

The curriculum...

This activity would be appropriate for a Grade 11 Physics class because it bridges between the Forces unit and the Waves and Sound unit.  Because of this, I think it would make an interesting culminating project for the course.

More critical...

My self-criticism for this idea is that although it may engage students and contains elements of the 21st Lesson Framework, I think it lacks any real critical analysis or underlying STSE issue; which I believe to be necessary for transformative pedagogy.    Maybe the instruments the students build could be made entirely of recycled materials to draw attention to the incredibly complex life cycle of manufactured goods we take for granted.  Anyways, it's something for me to think about for future entries.

21C...

1. Collaboration: entry - adoption - adaptation - infusion - transformation
2. Knowledge Construction: entry - adoption - adaptation - infusion - transformation
6. Use of ICT for Learning: entry - adoption - adaptation - infusion - transformation