Standing Waves on a String: Tension & Harmonics Lab
Change a string's tension and mass density to change its wave speed, then tune the driving frequency until it locks onto a harmonic and clean standing-wave loops appear.
Change the string's tension and mass density to change the wave speed, then tune the driving frequency until it locks onto a harmonic and clean standing-wave loops appear.
About the Standing Waves on a String: Tension & Harmonics Lab
Free standing waves on a string: tension & harmonics lab. Change a string's tension and mass density to change its wave speed, then tune the driving frequency until it locks onto a harmonic and clean standing-wave loops appear. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the standing waves on a string: tension & harmonics lab runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Change a string's tension and mass density to change its wave speed, then tune the driving frequency until it locks onto a harmonic and clean standing-wave loops appear. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Standing Waves on a String: Tension & Harmonics Lab
- Use the controls to change Tension T, Linear mass density μ (g/m), String length L, Driving frequency f. The simulation reacts instantly.
- Press "Reset to defaults", "Lab Report" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Tune the frequency slowly until the string locks into a clean standing wave.
- Find the third harmonic and count its nodes.
- Try the tension challenge to hit exactly 150 Hz on the third harmonic.
- Double the tension and check the fundamental frequency changes by √2, not 2.
Key ideas you can learn
- Wave speed on a string depends on its tension and mass per length: v = √(T/μ).
- A string fixed at both ends only resonates at specific harmonic frequencies, fn = n·v/(2L), where n = 1, 2, 3... counts the harmonic.
- At resonance, the string settles into a clean standing wave pattern with fixed nodes (no motion) and antinodes (maximum motion); away from resonance the pattern stays messy.
- Because v depends on the square root of tension, doubling the tension only increases wave speed - and every harmonic frequency - by a factor of √2, not 2.
Show my work
Challenges
Challenge 1 - hit the third harmonic at 150 Hz
Keep L = 1 m and μ = 2 g/m. Using v = √(T/μ) and fₙ = n·v/(2L), find the tension T (in newtons) needed so the third harmonic (n=3) is exactly 150 Hz. Set the tension slider to match and enter the value you used.
Challenge 2 - doubling the tension
If tension is doubled while everything else (μ, L) stays fixed, by what factor does the fundamental frequency f₁ change? (v ∝ √T, and f₁ ∝ v.) Enter the factor.
Where this is used in the real world
Every stringed instrument - guitars, violins, pianos - tunes pitch by changing string tension exactly according to v = √(T/μ), and engineers use the same standing-wave harmonic analysis for cables and bridge suspension lines.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
Why does a string only resonate at specific frequencies instead of any frequency?
Only wavelengths that fit an integer number of half-wavelengths exactly between the two fixed ends can form a stable standing wave, which restricts the allowed frequencies to fn = n·v/(2L).
Why does tightening a guitar string raise its pitch?
Raising the tension increases the wave speed v = √(T/μ), and since frequency is proportional to wave speed for a fixed string length, a higher wave speed directly raises every harmonic frequency, including the fundamental pitch you hear.
Is the Standing Waves on a String: Tension & Harmonics Lab free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Standing Waves on a String: Tension & Harmonics Lab work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.