Sound of the City: Standing Waves & Instrument Design
Frequency, wavelength, and resonance — inspired by the acoustics behind the Motown sound.
Name:
Class period:
Date:
Standards
HS-PS4-1 — Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves.
Why Does This Matter?
Motown's Hitsville U.S.A. studio, a few miles from most Detroit classrooms, built its signature sound using the acoustics of a small, echo-heavy room. Every note a Motown bassist played started with the same physics you'll measure today: string length, tension, and frequency.
Objective
Measure how the length of a vibrating string affects its frequency, then use that relationship to design a simple instrument tuned to specific notes.
Materials
- 1 rubber band or guitar string per group, stretched across a box or board
- Ruler
- Phone tuner app or tuning fork (teacher-provided)
- Pencil or small dowel (to act as a movable "fret")
- Data recording sheet (this handout)
Safety: Keep stretched rubber bands and strings pointed away from faces. Do not overstretch materials to the point of snapping.
Procedure
- Set up your string or rubber band under consistent tension across your box or board.
- Pluck the full-length string and use a tuner app to record its frequency.
- Place the pencil/dowel at the halfway point of the string, effectively shortening the vibrating length by half. Pluck and record the new frequency.
- Repeat for at least 3 more lengths (e.g. 3/4, 1/3, 1/4 of the original length), recording length and frequency each time.
- Graph frequency (y-axis) vs. string length (x-axis).
- Using your data, predict the string length needed to produce a target note your teacher assigns, then test your prediction.
Data Table
| Trial | String length (cm) | Frequency (Hz) | Musical note (if known) |
|---|---|---|---|
| 1 (full length) | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 (predicted) |
Analysis Questions
- Based on your graph, describe the relationship between string length and frequency in words.
- How close was your prediction for the target note to the actual measured frequency? What might explain any difference?
- A small, hard-walled room like Motown's Snakepit studio reflects sound waves quickly, reinforcing certain frequencies. How is that related to the standing waves you created on your string?
- If you wanted to build an instrument with a wide range of notes using only one string, what design feature would you need (hint: think about your dowel/fret)?