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Waves & Sound · Physics

Standing Waves Simulation

Two waves travelling opposite ways add up to a wave that stays put. See nodes and antinodes on strings and in open and closed pipes, drive a string until it resonates at its harmonics, and play a guitar string by moving your finger along the frets.

Interactive virtual lab · no download · works on phones and laptops

Chapter
Waves
For
Class 11 · JEE · NEET
Time
~12 min

Standing Waves is a Pro simulation

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How to use it

  1. 1Ends & pipes: choose a string, a closed pipe or an open pipe, and step through the harmonics.
  2. 2Make one: slowly raise the driving frequency and watch the string build up at each resonance.
  3. 3Guitar: pick a string, move the finger along the frets and listen.
  4. 4Turn on the travelling waves to see the two waves that make the standing one.

What to notice

  • A standing wave is two equal waves travelling in opposite directions; nodes never move, antinodes swing the most.
  • A string fixed at both ends, or an open pipe, has all harmonics: fₙ = n v / 2L.
  • A pipe closed at one end has only the odd harmonics: f = (2n − 1) v / 4L.
  • Shortening a string (pressing a fret) raises its frequency; 12 frets up doubles it.

For teachers

A ready-made teaching kit comes with this lab

  • Lesson plan

    21 min, 4 steps

  • Ask the class

    4 questions with answers

  • Quick quiz

    7 questions, printable

  • Key formulas

    4 formulas

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About the Standing Waves simulation

A standing (stationary) wave forms when two identical waves travel through each other in opposite directions — usually a wave and its own reflection. Their sum doesn't travel: some points, the nodes, never move, and the points halfway between, the antinodes, swing the most. Only certain wavelengths fit between the ends, which is why strings and pipes have definite notes.

This standing waves simulation has three screens. Ends & pipes shows the harmonics of a string fixed at both ends, a pipe closed at one end and an open pipe, with the two travelling waves that make each one. Make one drives a string at any frequency so you can watch it build up at resonance. Guitar lets you fret six strings and hear the notes. It covers Waves in Class 11 — the sonometer, organ pipes and resonance-tube questions in JEE and NEET.

Also covers: standing waves, stationary waves, nodes and antinodes, harmonics, overtones, open pipe, closed pipe, organ pipe, sonometer, guitar string, resonance.

Frequently asked questions

What is the difference between a standing wave and a travelling wave?

A travelling wave carries energy along; in a standing wave the two opposite waves balance, so the pattern stays in place with fixed nodes and antinodes.

Why does a closed pipe have only odd harmonics?

It needs a node at the closed end and an antinode at the open end, so its length must be an odd number of quarter-wavelengths: L = (2n − 1)λ/4.

How far apart are two neighbouring nodes?

Half a wavelength. A node and the nearest antinode are a quarter-wavelength apart.

Why does pressing a guitar string at a fret raise the note?

It shortens the vibrating length, and f = (1/2L)√(T/μ) rises as L falls. Halving the length (the 12th fret) doubles the frequency.

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