Using Guitars to Teach Algebra and Physics

Years ago, I used to teach high school math courses. Using an interdisciplinary approach with the course content aided students in synthesizing the material and getting a deeper understanding of its purpose, especially abstract mathematics.

One of my interdisciplinary lessons was on the topic of calculating the Harmonic Mean. Many students have a distaste for using fractions, especially reciprocals. Students showed much more interest in this topic by using a story and relating the content to history, religion and music. I brought a guitar to class and began the lesson by telling them about Pythagorus of Samos and his clan of friends, the Pythagoreans who lived on the Greek island of Samos. They created a type of cult or religion whose foundation was relating music to math, more specifically ratios. Some historians claim that the Pythagoreans believed that if one could truly understand the meaning of "wholeness" they would be immortal. After telling this story, I took out a guitar and often had one of my students show to find harmonics on a guitar string. Another student would get a metre stick and we would measure ratios of notes on a single string and record harmonics.

I enjoyed this lesson so much in my math classes it is now adapted it for my grade 11 Physics course. It fits well with the Sound unit, when we cover the topics of harmonics and tones. This lesson truly gets students to see how mathematics and physics relate to music. I have taken this lesson one step further in my Physics class. Students use the computer program Audacity to create an audio project with separate labeled audio tracks that clearly depict different sound waves (loud notes, quiet notes, high notes, low notes, tone and harmonics). Students narrate additional tracks to explain what the sine waves mean. Once identical twins were in my class. They recorded themselves saying the same phrases in the same way. Even I was surprised with how closely their resulting sines waves appeared.