Teaching Objectives
- Introduce basic wave properties like amplitude, wavelength, period, and frequency
- Teach the relationship between period and frequency
- Connect the concept of frequency to pitches
- Teach the frequency formula for strings
- Demonstrate all the variables that can affect pitch (string length, string tension etc, string density) through example
- Teach interference through pythagorean ratios and harmony
- Demonstrate practicality by creating an instrument that was created using the pythagorean ratios and the frequency formula for strings
Pedagogy
Why Start with Music?
Music is a compelling entry point because most students, regardless of background, have a personal connection to music, whether through listening, playing, or cultural experiences. This familiarity lowers the barrier of entry and makes the physics feel more accessible. By showing that music is governed by wave physics, students will hopefully see science not just as abstract equations but as something that explains their everyday world. The purpose is not to "teach music," but to use it as a framework to uncover the physics that underpins it.
Framing the Wave Concept
Once the students are engaged, I introduce the concept of a wave—not as a formula, but as a repeating pattern of motion. This is scaffolded by everyday examples: ripples in water, earthquakes, or even visible light. The goal here is to build an intuitive sense of what a wave *is* before we ever quantify it. The pedagogical purpose is to help students "see" waves in action before abstracting them into symbols.
From Perception to Measurement
Next, I introduce basic wave properties in an intresting way by connecting musical concepts to measurable physical properties. Pitch becomes frequency. Volume becomes amplitude. By relating physical properties to perceptions students already understand, we remove the mystery from the terms.
Harmony, Interference, and Mathematical Beauty
Next, we explore how harmony arises from wave interference. I tell the story of Pythagoras and his experiments with string ratios. Using two strings tuned in a 2:1 ratio, we explore why octaves sound consonant. The same goes for 3:2 (perfect fifth), and so on. The goal isn't just to show musical intervals—it's to demonstrate that mathematical relationships lead to aesthetic experiences. This frames physics as a tool for understanding beauty, not just solving problems. More on this on a youtube link below.
Connecting Theory to Tension, Mass, and Length
Now that students appreciate the sensory outcomes, we dive into the physics of string vibration. Using a modifed version of the wave equation and the frequency board demo, I show how string frequencies are not only about length, but also about tension and its linear mass density. The goal is to allow students a framework to predicting physical phenomenon and not just observe it. Students will hopefully connect abstract concepts to real, physical variables they can manipulate.
An Instrument to tie it all together
To synthesize everything, I use a homemade lyre. This instrument, while not perfect, embodies all the wave principles we've studied. The strings vary in length, thickness, and tension to create different frequencies. Then, I play a short melody to tie it all together. It demonstrates the intersection between physics and music.
Conclusion: Why This Approach Works
Rather than presenting waves as an abstract topic, music is used to ground the discussion in human experience. Students will connect formulas to something that is measurable and quantifiable in their daily life