Harmonics on a String
Lesson notes
Overview
Plucked strings vibrate in whole-number multiples of the fundamental frequency. This topic is rated intermediate and is number 42 of 227 in Physics. Builds on the basics with relationships, methods and trade-offs.
What you are seeing
The panel above shows a wave travelling and interfering, with sliders for frequency and amplitude. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
A plucked string vibrates in the fundamental mode and in many overtones at the same time. The allowed frequencies are whole-number multiples of the fundamental, f_n = nf₁, called harmonics. The mixture of harmonics gives an instrument its tone colour, which is why a violin and a flute playing the same note sound different. Shortening the string, tightening it or using a lighter string raises the fundamental.
Reading the relationship
The expression "f_n = n f₁" is a compact summary of the idea. It uses the symbols f_n, n, f₁; name what each one stands for before you start. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Start with a single wave and measure its wavelength and period. 2. Change frequency and amplitude separately. 3. Add a second source or reflection and watch the waves combine.
Try this
Predict the outcome first, then test extreme slider values to find where the pattern changes or breaks.
Common pitfalls
Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.
How it connects
It builds on “Standing Waves”, the topic before it in Physics. Once you are comfortable, continue with “Beats”.
Why it matters
Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.
Where you might use it
- Revising “Harmonics on a String” before a class, exam or certification
- Designing vehicles, bridges and devices where motion, forces or waves must be predicted
- Understanding how sensors, lasers and communication links actually work
- Explaining everyday phenomena such as sound, light, heat and orbits
Frequently asked questions
What is Harmonics on a String?
Plucked strings vibrate in whole-number multiples of the fundamental frequency. It is an intermediate topic in Physics.
How do I use the Harmonics on a String simulation?
The panel at the top shows a wave travelling and interfering, with sliders for frequency and amplitude. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression f_n = n f₁ packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Builds on the basics with relationships, methods and trade-offs. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Standing Waves”, the previous topic in Physics. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.