Monochord Lab Sheet (Age 13)
Goal: Explore how changing the length and tension of a vibrating string changes pitch (frequency), and discover simple musical intervals using a monochord.
Materials
- Monochord (a single string stretched over a wooden box or board with a movable bridge), or: a strong string tied across a wooden ruler or board and a movable bridge (a small block of wood or pencil can work)
- Stand or clamp to hold the string ends, or heavy fixtures for end points
- Small masses or spring scale to change/measure tension (optional)
- Ruler or measuring tape (mm or cm)
- Tuning app or frequency meter on a phone (optional) or a piano/tuning fork to compare pitch
- Pencil or pick to pluck the string
- Notebook and pen for observations
- Safety goggles (if using clamps or weights)
Background (Simple)
A monochord is a single string that you can shorten by moving a bridge under the string. When you pluck the string, it vibrates and produces a sound. The pitch of that sound depends on three things:
- Length of the vibrating part of the string (L)
- Tension in the string (T)
- Mass per unit length of the string (μ) — how heavy the string is per centimeter)
For this lab we will mostly change L (by moving the bridge) and sometimes change T (by adding weight). A key idea: when tension and mass per length stay the same, frequency (pitch) is inversely proportional to length. So if you halve the length, the frequency doubles and the note goes up one octave.
Important Formula (for teacher reference)
f = (1 / 2L) × sqrt(T / μ). You do not need to rearrange this for the lab, but remember: if L goes down, f goes up.
Safety
- Wear goggles if using clamps or weights that could slip.
- Make sure the string and setup are secure to avoid slippage or snapping.
Procedure (Step-by-step)
- Set up the monochord so the string is tight and can vibrate freely between two fixed end points. Measure and record the total vibrating length L0 (in cm).
- Pluck the string at a point near 1/4 from an end and listen. Use a tuner app to measure the fundamental frequency f0 if available. Record f0 and any note name you hear.
- Place the movable bridge at half of L0 (L = 1/2 L0). Make sure the bridge holds firmly. Pluck the shorter string and record the frequency f_half or the note name. Note any change in pitch. Predict what will happen before you pluck.
- Move the bridge to lengths corresponding to simple fractions of L0: 2/3 L0, 3/4 L0, and 1/3 L0. At each position pluck the string, record the frequency or the note and describe how the sound changed.
- If you have a mass to change tension, keep the length fixed (for example at L0) and add a known weight to increase tension. Pluck and record how the pitch changed.
- Repeat any measurements 2–3 times and average the frequencies if you used an app.
Data Table (fill in during lab)
| Trial | Bridge Position (length L, cm) | Fraction of Original Length (L/L0) | Measured Frequency (Hz) | Observed Note (or relative 'higher'/'lower') | Frequency Ratio (f / f0) | Comments |
|---|---|---|---|---|---|---|
| 1 (full) | _____ | 1.00 | _____ | _____ | 1.00 | Fundamental |
| 2 (half) | _____ | 0.50 | _____ | _____ | _____ | Expect octave if tension same |
| 3 (2/3) | _____ | 0.67 | _____ | _____ | _____ | Expect perfect fifth (approx) |
| 4 (3/4) | _____ | 0.75 | _____ | _____ | _____ | Expect perfect fourth (approx) |
| 5 (1/3) | _____ | 0.33 | _____ | _____ | _____ | Higher pitch (triads) |
Example Calculation (to help)
Suppose full length L0 = 60 cm and you measured f0 = 220 Hz at that length. If you place the bridge at L = 30 cm (half), then you expect frequency f = (L0 / L) × f0 = (60 / 30) × 220 = 2 × 220 = 440 Hz. That is exactly one octave higher.
Why the Fractions Make Musical Intervals
- Length 1/2 → frequency 2/1 → octave (same note, higher)
- Length 2/3 → frequency about 3/2 → perfect fifth
- Length 3/4 → frequency about 4/3 → perfect fourth
These ratios are why musical intervals sound pleasant: the waves line up regularly at simple ratios.
Analysis Questions (Answer in your lab notebook)
- Describe how the pitch changed when you halved the length. Did the tuner show double the frequency? Explain in simple words why.
- Compare the measured frequency ratios to the expected ratios (2:1, 3:2, 4:3). How close were your measurements? What might cause differences?
- What happened to pitch when you increased tension? Did it go up or down? Why, using the formula idea?
- If you used a thicker or thinner string, how would μ change and what effect would that have on frequency?
- How could you produce a major third (roughly ratio 5:4) on the monochord? (Hint: try setting the length to 4/5 of original.)
Possible Sources of Error
- Bridge slipping or not holding the string firmly.
- Inaccurate length measurements.
- Changing tension when moving the bridge slightly.
- Imprecise frequency app measurements (background noise).
Extensions and Creative Ideas
- Try making chords by plucking two sections at once (if your setup allows two bridges).
- Compare two different strings (steel vs nylon) and see differences in pitch for same length and tension.
- Use a microphone and sound analysis software to see harmonics (overtones) on the string.
- Design an experiment to measure the relationship between tension and frequency quantitatively (keep L and μ constant and measure f for several tensions).
Conclusion (What to write after the lab)
Summarize your main findings: how pitch changed with length and tension, whether your measured frequency ratios matched musical interval ratios, and what you learned about waves and sound. Mention any surprising results and possible improvements.
Have fun exploring sound with the monochord!