Understanding Stationary Waves: A Comprehensive Guide

Oct 21, 2025

3 min read

What are Stationary Waves?

Stationary waves are formed when two identical waves travel in opposite directions and interfere with each other. This often occurs when a wave is reflected back on itself, such as on a string fixed at both ends.

The waves superpose (combine) — in some places, they reinforce each other (constructive interference), while in others, they cancel out (destructive interference).
The result is a wave pattern that appears to stand still: nodes and antinodes remain in fixed positions.

Key Features of Stationary Waves

Nodes: Points that stay still (complete destructive interference, zero amplitude).
Antinodes: Points that vibrate with maximum amplitude (complete constructive interference).

Stationary wave showing nodes and antinodes

No net energy transfer: Unlike travelling waves, stationary waves do not transport energy from one end to the other.
Depend on wavelength & boundary conditions: Only certain frequencies produce stationary waves — these are called the resonant frequencies.

Everyday and Scientific Examples

Musical Instruments
Guitar strings, violin strings, and organ pipes all produce stationary waves.
The pitch (frequency) depends on the length of the string or pipe, the tension, and the wavelength.

Microwave Ovens
Stationary waves form inside the oven cavity.
This is why some areas heat more strongly (antinodes) while others are cooler (nodes).
That’s also why microwaves often have a turntable — to move food through the nodes and antinodes.

Resonance in Air Columns
Wind instruments (flutes, clarinets, trumpets) use stationary waves in columns of air.
The length of the air column sets the note produced.

Physics & Materials Testing
Stationary waves can be used to study resonance in materials and detect flaws by how waves reflect and interfere.

Why are Stationary Waves Important in Applied Science?

Stationary waves are crucial for several reasons:

They explain how musical instruments and sound engineering work.
They are central to understanding resonance phenomena in physics.
They apply in engineering (vibration analysis, testing structures).
They link to wave theory more broadly, helping you master Unit 1 content on oscillations and wave behaviour.

Sample Exam Question (6 marks)

Question:

Musical notes are sound waves and can be produced by plucking strings or blowing through a pipe. Compare the waves produced on a string with those produced in an open pipe.

Model Answer

Draw an image of a wave in a string and a wave in an open pipe, labelling the nodes and antinodes.

Explain the number and arrangement of nodes and antinodes in each case.

Waves on a string have a node at each end. Waves in an open tube have antinodes at each end. On a string, the number of nodes is one more than the number of antinodes. In an open tube, the number of nodes is one less than the number of antinodes.

Compare the types of wave formed on strings and in pipes.

The lowest frequency that can be produced on a stretched string (the fundamental frequency) occurs when the wavelength is 2L, where L is the length of the string. For an open pipe, the lowest frequency is also the fundamental, and this occurs when the wavelength of the standing wave is 2L, with L representing the length of the pipe.

Key Notes

A stationary wave forms because two identical waves travel in opposite directions and superpose.

String	Open pipe

Nodes = zero displacement (fixed points) Antinodes = maximum displacement A string always has nodes at both ends	Open ends are always antinodes because the air is free to move. An open pipe has the same harmonic rules as a fixed–fixed string.