PhysicsMechanical WavesUniversity
IBUndergraduate

Standing Wave Function Calculator

Calculates the displacement of a standing wave from position and time.

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Wave displacement

Formula first

Overview

A standing wave can be written as a product of a position-dependent shape and a time-dependent oscillation. Nodes occur where sin(kx)=0, so those points stay at zero displacement.

Symbols

Variables

f = Wave displacement, A = Amplitude of each travelling wave, kx = Position phase, t = Time phase

Wave displacement
Amplitude of each travelling wave
kx
Position phase
rad
Time phase
rad

Apply it well

When To Use

When to use: Use this for ideal standing waves formed by two equal-amplitude waves traveling in opposite directions.

Why it matters: Standing-wave functions describe strings, air columns, normal modes, and resonance patterns.

Avoid these traps

Common Mistakes

  • Putting degrees into the trig functions.
  • Treating a standing wave as if the pattern travels sideways.

One free problem

Practice Problem

For A=0.020 m, kx=pi/2, and omega t=0, what is the displacement?

Amplitude of each travelling wave0.02 m
Position phase1.5707963268 rad
Time phase0 rad

Solve for: waveDisplacement

Hint: Use y = 2A sin(kx) cos(omega t).

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Moebs, Ling, and Sanny, University Physics Volume 1, OpenStax, 2016, section 16.6, accessed 2026-04-09
  2. Wikipedia: Standing wave (accessed 2026-04-09)
  3. NIST CODATA Value
  4. IUPAC Gold Book
  5. Wikipedia: Standing wave
  6. University Physics, Volume 2 by OpenStax
  7. Feynman Lectures on Physics, Vol. 1
  8. Introduction to Electrodynamics by David J. Griffiths