The big idea: Twang a guitar string, or shake a skipping rope at just the right speed, and it settles into a row of loops that sits still on the spot. That fixed pattern is a standing wave.
How it forms
- Some points blur with motion; others never move at all.
- It forms when two identical waves travel in opposite directions and add up.
- Usually it is a wave and its own reflection off a fixed end.
- The points that never move are nodes; the points that swing the most are antinodes.
- Superposition
- when two waves overlap, you add their displacements at every point to get the total.
- Standing (stationary) wave
- the fixed pattern made by two identical waves travelling in opposite directions; it does not move along.
- Node
- a point that never moves (always zero displacement) — the two waves always cancel there.
- Antinode
- a point that swings with the biggest amplitude, halfway between two nodes.
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Spot the parts: Node = no motion (stays at zero) · antinode = maximum motion.
Neighbouring nodes are half a wavelength (λ/2) apart — so do the antinodes.
How the two waves add
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A standing wave behaves very differently from a normal travelling wave. The two big differences the exam tests are energy and phase.
Travelling wave
- The pattern moves along
- Carries energy from place to place
- Every point has the same amplitude
- The phase keeps shifting point to point
Standing wave
- The pattern stays put
- Carries no net energy along it
- Amplitude varies: zero at nodes, max at antinodes
- Points are either in phase or antiphase — nothing in between
New word — phase: Phase means where a point is in its swing — moving up, moving down, at the top, etc.
On a standing wave, every point between two nodes moves in phase (together). Points on opposite sides of a node move in antiphase (exactly opposite — one up while the other is down).
Amplitude, phase and longitudinal standing waves: The amplitude varies along a standing wave: zero at a node, largest at an antinode, in between elsewhere.
In a pipe or a rod the particles move along its length. Draw the pattern as the envelope of how far they move: a rod free at both ends (like a pipe open at both ends) in its first harmonic has antinodes at both ends and a node in the middle. Atoms on opposite sides of that node move in antiphase.
Sand or dust in a tube collects at the displacement nodes, where the air does not move.
No formula in the data booklet — so remember this: There is no standing-wave equation in the data booklet. The one fact to remember is the spacing:
adjacent nodes (and adjacent antinodes) are half a wavelength, λ/2, apart.
So measure node-to-node, double it, and you have the wavelength λ — then use the given wave equation v = fλ.
- wave speed (m s⁻¹)
- frequency — waves per second (Hz)
- wavelength — length of one full wave (m)
On a vibrating string the distance from one node to the next node is 0.30 m. Find the wavelength of the wave.
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How this is tested — standing waves come up as concept questions and one classic application:
Paper 1A
- Compare two points on a standing wave (in phase or antiphase) with two points on a travelling wave (phase shifts smoothly).
Paper 2
- Outline how a standing wave forms a fixed pattern of hot spots — the famous microwave-oven question (melted spots sit at the antinodes).
The classic trap: Thinking a standing wave carries energy along it. It does not — it just stores energy in place.
The microwave-oven story: Microwaves reflect off the metal walls. The reflected wave meets the incoming one and they superpose into a standing wave that sits still inside the oven.
The field is strongest at the antinodes, so food melts there first; at the nodes the field is always zero, so those spots stay cold. (That's why ovens use a turntable.)
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A bar of chocolate is heated in a microwave oven with the turntable removed. After a short time, melted spots appear in an evenly spaced row. Outline how this pattern forms.
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