The big idea: Send two identical waves along the same string in opposite directions and they add up into a fixed pattern that does not travel along — a standing wave.
The pattern has points that never move (nodes) and points that swing the most (antinodes).
The usual way to make one: a wave reflects off a fixed end and meets itself coming back.
- 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.
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.
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).
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)
Worked example — wavelength from the node spacing
On a vibrating string the distance from one node to the next node is 0.30 m. Find the wavelength of the wave.
Solution
- Remember the spacing rule — neighbouring nodes are half a wavelength apart:
- Put in the measured spacing (0.30 m):
- Double it to get the wavelength — keep the unit:
Final answer
wavelength λ = 0.60 m (twice the node-to-node spacing).
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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).
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.)
IB-style question — outline how the melt pattern forms
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.
Solution
- Two waves, opposite ways — the microwaves reflect off the metal walls, so a reflected wave travels back against the incoming wave.
- They superpose into a standing wave — the two identical waves add up to a fixed pattern of nodes and antinodes that does not move along the oven.
- Antinodes get hottest — at the antinodes the microwave field is strongest, so the chocolate absorbs the most energy and melts there.
- Nodes stay cold — at the nodes the field is always zero, so those spots stay solid; melted spots are one antinode apart (half a wavelength).
Final answer
Reflected and incoming microwaves superpose into a standing wave; the chocolate melts at the antinodes (strong field) and stays solid at the nodes, giving an evenly spaced row of melts.