Stationary Waves

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Explain and use the principle of superposition
  2. Show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns
  3. Explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes
  4. Understand how wavelength may be determined from the positions of nodes or antinodes of a stationary wave

1. The Principle of Superposition

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What is Superposition?

When two or more waves meet at the same point in space, they overlap. This overlapping is called superposition.

The Principle of Superposition states:

When two or more waves overlap at a point, the displacement at that point is equal to the sum of the displacements of the individual waves.

In simpler terms: when waves meet, their heights (or depths) add together to create a new combined wave at that moment.

How Superposition Works

  • Wave displacements can be positive (upward) or negative (downward)
  • When adding displacements, you combine them like you would with any numbers:
    • Positive + Positive = Larger positive (waves reinforce each other)
    • Negative + Negative = Larger negative (waves reinforce each other)
    • Positive + Negative = They partially or completely cancel out

Example: If Wave 1 has a displacement of +3 cm at a point, and Wave 2 has a displacement of +2 cm at the same point, the resultant displacement is +5 cm.

If Wave 1 has +3 cm and Wave 2 has -3 cm at the same point, the resultant displacement is 0 cm (they cancel out completely).

Superposition in Action

Imagine two pulses (wave bumps) traveling toward each other on a rope:

  • Before they meet: Each pulse travels independently
  • As they meet: Their displacements add together (superposition occurs)
  • After they pass: Each pulse continues on its way as if nothing happened

The waves don't permanently change each other—they just temporarily combine when they overlap.

2. What are Stationary Waves?

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Definition

A stationary wave (also called a standing wave) is a wave pattern that appears to stay in one place rather than traveling along.

How Stationary Waves Form

Stationary waves are produced when:

  1. Two waves of the same frequency and similar amplitude travel in opposite directions
  2. These two waves superpose (overlap and combine)
  3. Usually, one wave is the original wave and the other is its reflection from a boundary

The result is a wave pattern that doesn't appear to move along—instead, certain points vibrate up and down while others stay completely still.

Key Difference from Progressive Waves

  • Progressive wave: The wave pattern moves along, transferring energy from one place to another
  • Stationary wave: The wave pattern stays in the same place; there is no net transfer of energy along the wave

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