Free Physics Simulation

Explore the Standing Waves on a String: Tension &

Change a string's tension and mass density to change its wave speed, then tune the driving frequency until it locks onto a harmonic.

Try it free See how it works

Free to use
No signup
Nothing to install
Runs in your browser

Free to use

No signup

Standing Waves on a String: Tension &

Setting

Open the Standing Waves on a String: Tension &

Illustration. Open the tool for the real thing.

See it in action

The Standing Waves on a String: Tension & with sample data entered and the result showing.

Screenshot of the Standing Waves on a String: Tension & with sample data entered: The Standing Waves on a String: Tension & with sample data entered and the result showing. — Sample data entered into the Standing Waves on a String: Tension &. Open the tool to try your own.

Explained

What is the Standing Waves on a String: Tension &?

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. It runs in your browser, so a change to a setting or a drag on an object shows up at once.

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.

Try it free

Key idea 1Key idea 2Key idea 3

3 steps to your result

Open the tool and follow along. Nothing to install.

In 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.

Start with this experiment: Tune the frequency slowly until the string locks into a clean standing wave. Drag any glowing handle, object or slider with your mouse or finger and the Standing Waves on a String: Tension & Harmonics Lab responds in real time.

Change one setting at a time and watch which readout moves, then compare it with this idea: Wave speed on a string depends on its tension and mass per length: v = √(T/μ).

What you get

Key idea 1

Wave speed on a string depends on its tension and mass per length: v = √(T/μ).

Key idea 2

A string fixed at both ends only resonates at specific harmonic frequencies, fn = n·v/(2L), where n = 1, 2, 3... counts the harmonic.

Key idea 3

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.

Experiment 1

Tune the frequency slowly until the string locks into a clean standing wave.

Experiment 2

Find the third harmonic and count its nodes.

Experiment 3

Try the tension challenge to hit exactly 150 Hz on the third harmonic.

Used for

Pick one to see how it fits.

Use case

Physics learners

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.

Try it free

How it compares

A plain look at this tool next to the usual alternative.

	This simulation	Textbook diagram
Interactive	Drag, tap and change settings	Fixed picture
Install	Nothing to install	Not needed
Cost	Free to use	Depends on the book

Questions people ask

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. The Standing Waves on a String: Tension & Harmonics Lab is free, needs no signup or download and runs in your web browser. It is part of the Physics group of AZRS simulations.

Does the Standing Waves on a String: Tension & Harmonics Lab work on a phone or tablet?

Yes. The Standing Waves on a String: Tension & Harmonics Lab takes touch input as well as mouse input, so you can use its 4 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.

How do I use the Standing Waves on a String: Tension &?

1. In 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. 2. Start with this experiment: Tune the frequency slowly until the string locks into a clean standing wave. Drag any glowing handle, object or slider with your mouse or finger and the Standing Waves on a String: Tension & Harmonics Lab responds in real time. 3. Change one setting at a time and watch which readout moves, then compare it with this idea: Wave speed on a string depends on its tension and mass per length: v = √(T/μ).