Look closely at a standing wave and you’ll spot two very different kinds of places: points that never move at all, and points that swing harder than anywhere else. These are the nodes and antinodes — and once you can find them, you can read a standing wave like a map.
📘 What you need to know
A node is a point of zero amplitude — it stays completely still the whole time
An antinode is a point of maximum amplitude — it oscillates with the biggest swing
Nodes and antinodes do not move along the wave — nodes are fixed, and antinodes only oscillate vertically on the spot
Adjacent nodes are half a wavelength (λ/2) apart; a node and its neighbouring antinode are λ/4 apart
Nodes form where the two waves meet in anti-phase (destructive interference); antinodes form where they meet in phase (constructive interference)
Two points on a standing wave are either exactly in phase or exactly in anti-phase — nothing in between
Meet the Nodes and Antinodes
Picture the standing wave on a string as a chain of vibrating loops. Between every pair of loops sits a point that never budges — that’s a node. And right in the middle of each loop is the point doing all the hard work, swinging up and down through the biggest distance — that’s the antinode.
Here’s the key idea: unlike a travelling wave, where the crests march along the string, on a standing wave everything stays where it is. The nodes are pinned in place, and the antinodes bounce up and down without going anywhere sideways.
Nodes (red dots, N) sit where the solid and dashed curves cross the axis — they never move. Antinodes (A) sit in the middle of each loop and swing between the solid and dashed positions. Node to node is λ/2, so one full wavelength covers two loops.
Why Nodes and Antinodes Form
Remember, a standing wave is really two travelling waves passing through each other. At every point on the string, the two waves add together — but how they add depends on where you are.
At a node, the two waves always arrive in anti-phase: whenever one wave says “up”, the other says “down” by exactly the same amount. A crest from one wave meets a trough from the other, and they cancel out. This is destructive interference — the total displacement is always zero, so the point never moves.
At an antinode, the two waves always arrive in phase: crest meets crest, and trough meets trough. They add together, giving double the effect. This is constructive interference — so the point oscillates with maximum amplitude.
crest meets trough
destructive interference
cancel out
gives a
NODE
crest meets crest
constructive interference
add together
gives an
ANTINODE
The Spacing Rule
The pattern of nodes and antinodes is beautifully regular, and it hides the wavelength in plain sight:
Node spacing
distance between adjacent nodes = λ ÷ 2
So one loop = half a wavelength, and you need two loops to make one full wavelength. The same rule applies to adjacent antinodes — they’re also λ/2 apart. And since an antinode sits exactly halfway between two nodes, the distance from a node to the nearest antinode is λ/4.
This is the single most useful fact on this page: if an exam question shows you a standing wave picture, count the loops, and the wavelength follows immediately.
Phase on a Standing Wave
On a travelling wave, phase changes smoothly from point to point — two points can be out of step by any amount from 0 to 2π. Standing waves are much stricter. Two points are either:
in phase — they move up together and down together, or
in anti-phase — when one is up, the other is down (π out of phase)
And there’s a simple counting trick to tell which is which:
Points inside the same loop are always in phase
Points separated by an odd number of nodes (1, 3, 5…) are in anti-phase
Points separated by an even number of nodes (2, 4, 6…) are in phase
Count the nodes between two points: an even number (including zero) means in phase, an odd number means anti-phase. Here A, B and D all move together, while C always does the opposite.
🎨 How to draw a standing wave in the exam
Axis first — draw a horizontal line for the equilibrium position, with a firm boundary at each fixed end
Draw the loops — smooth, even loops sitting on the line, like a chain of stretched eyes; every loop must touch the axis at both ends
Add the mirror image — draw the same loops dashed, flipped below the line (this shows the string half a cycle later)
Mark the nodes — a dot everywhere the curves cross the axis, including the fixed ends
Mark the antinodes — at the widest point of each loop, halfway between nodes
Label a spacing — write λ/2 between two adjacent nodes so the examiner sees you know the scale
Quick recap: node = zero amplitude (destructive interference), antinode = maximum amplitude (constructive interference). Adjacent nodes are λ/2 apart, and phase on a standing wave is only ever 0 or π.
WE 1
A standing wave on a string of length 1.2 m has 6 nodes, including one at each fixed end.
(a) Calculate the distance between adjacent nodes.
(b) Determine the wavelength of the waves on the string.
Part (a)
6 nodes means 5 loops fit on the string
node spacing = 1.2 ÷ 50.24 mPart (b)
Adjacent nodes are λ/2 apart, so
λ = 2 × 0.24λ = 0.48 mBonus check: node to nearest antinode would be λ/4 = 0.12 m.
WE 2
P, Q and R are three points on a standing wave. P and Q sit in the same loop. R is in the loop next to P’s, so there is one node between P and R. State the phase relationship between (a) P and Q, and (b) P and R.
Part (a)
P and Q are in the same loop — zero nodes between them (an even number)
P and Q are in phasePart (b)
P and R have one node between them (an odd number)
P and R are in anti-phaseIn anti-phase means π out of phase: when P is at its highest, R is at its lowest.
💡 Top tips
Memory trick: a NOde is where there’s NO motion
Count loops to find the wavelength: one loop = λ/2, so λ = 2 × (node spacing) — the most-used fact in standing wave questions
Phase on a standing wave can only be 0 or π; travelling waves can have any phase difference from 0 to 2π — a favourite multiple-choice trap
The number of antinodes always equals the number of loops, and (for a string fixed at both ends) nodes = loops + 1
⚠ Common mistakes
Taking the node-to-node distance as a full wavelength — it’s only half of one
Measuring node-to-antinode as λ/2 — that’s the λ/4 distance
Saying nodes and antinodes “move along the string” — they stay exactly where they are
Applying travelling-wave phase rules to a standing wave — on a standing wave there’s no gradual phase change, only 0 or π
Up next: boundary conditions — how fixed ends, free ends, and open or closed pipes decide where the nodes and antinodes are allowed to sit.
Want this to actually click before the exam?
Book a free meeting and let’s work through the tricky bits together.
