Home · A-Level 9702 · Superposition · Stationary waves · Practice
AS · Practice questions · Stationary waves

Standing still.

Six original Cambridge-style questions on superposition, node spacing, and harmonics.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Nodes are half a wavelength apart.

01
Analysis
[2 marks]

State the principle of superposition.

  • When two or more waves meet at a point, the resultant displacement is the vector sum of the individual displacements ✓
02
Analysis
[2 marks]

Distinguish between a node and an antinode on a stationary wave.

  • A node is a point of permanently zero amplitude ✓
  • An antinode is a point of maximum amplitude ✓
03
Analysis
[2 marks]

On a stationary wave the adjacent antinodes are 0.25 m apart. Find the wavelength.

  • Adjacent antinodes are λ/2 apart ✓
  • λ = 2 × 0.25 = 0.50 m ✓
04
Analysis
[3 marks]

A string of length 1.2 m is fixed at both ends and vibrates in its fundamental mode. Find the wavelength of the wave on the string.

  • The fundamental has a node at each end and one antinode, so the length is half a wavelength ✓
  • λ = 2L = 2 × 1.2 = 2.4 m ✓
05
Analysis
[2 marks]

State two ways in which a stationary wave differs from a progressive wave.

  • A stationary wave does not transfer energy along its length, while a progressive wave does ✓
  • A stationary wave has fixed nodes and antinodes, whereas every point on a progressive wave has the same amplitude ✓
06
Analysis
[3 marks]

Microwaves reflected from a metal sheet form a stationary wave with nodes 1.5 cm apart. Taking c = 3.0 × 10⁸ m s⁻¹, find the wavelength and frequency.

  • λ = 2 × node spacing = 2 × 0.015 = 0.030 m ✓
  • f = c / λ = (3.0 × 10⁸) / 0.030 = 1.0 × 10¹⁰ Hz ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.