AQA | A Level | 7408

Stationary Waves

Written by: Katie M
Reviewed by: Ashika Raveendran
Updated on 14 March 2025

Stationary Waves on Strings

A stationary wave is formed when two progressive waves travelling in opposite directions with the same frequency and amplitude are superposed
Points on a stationary wave oscillate with different amplitudes
Nodes are points of zero amplitude (no oscillation)
Antinodes are points of maximum amplitude

Formation of Stationary Waves

When a stretched string is plucked, progressive waves travel along the string and are reflected at the fixed ends. The incident and reflected waves superpose to create a stationary wave pattern.

The distance between adjacent nodes (or adjacent antinodes) is half a wavelength
All points between two adjacent nodes oscillate in phase with each other
Points on either side of a node oscillate in antiphase

Worked Example

A stretched string is used to demonstrate a stationary wave, as shown in the diagram.

Which row in the table correctly describes the length of L and the name of X and Y?

	Length L	Point X	Point Y
A	5 wavelengths	Node	Antinode
B	2½ wavelengths	Antinode	Node
C	2½ wavelengths	Node	Antinode
D	5 wavelengths	Antinode	Node

Answer: C

Step 1

Calculate how many wavelengths in the length of the string
There are 2½ complete wavelengths visible. This rules out A and D.

Step 2

X is a point of zero displacement - a node

Step 3

Y is a point of maximum displacement - an antinode

Step 4

The correct row is C

Exam Question

Stationary Waves

A guitar string of length 0.65 m is plucked and vibrates in its third harmonic.

(a) Calculate the wavelength of the stationary wave.

(b) Explain why the points at the bridge and nut of the guitar must be nodes.

[4 marks]

3/4

Good attempt

(a) Correct: For the third harmonic, L = 3(λ/2), so λ = 2L/3 = 2(0.65)/3 = 0.433 m

(b) You correctly identified that the bridge and nut are fixed points.

(b) Missing: You need to state that fixed points cannot oscillate, so they must have zero amplitude, which is the definition of a node.

Exam Question

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The frequency of a stationary wave depends on the tension in the string, its length, and its mass per unit length.

Examiner Tips and Tricks

Make sure you can distinguish between progressive waves and stationary waves. A common exam question asks you to compare the two in terms of energy transfer, phase, and amplitude.

Harmonics

The fundamental frequency (first harmonic) is the lowest frequency mode of vibration
Higher harmonics are whole-number multiples of the fundamental
The nth harmonic has n antinodes and (n + 1) nodes (including the two fixed ends)

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Stationary Waves