Stationary Waves
Physics: AQA A Level, topic 3.1.6
Stationary Waves
Stationary waves are important physical concepts. They can be created when a wave interferes with its reflection.
Definition
- A stationary wave is formed when two progressive waves, each with the same frequency and wavelength and moving in opposite directions, interfere with one another.
- This creates a wave which doesn't transfer energy from one place to another.
Nodes
- Nodes are points on a stationary wave that have zero amplitude.
- Having zero amplitude means that they are stationary.
Antinodes
- Antinodes are points on a stationary wave with maximum amplitude.
- They oscillate from the furthest point upwards to the furthest point downwards.
Resonance and Harmonics
Stationary waves can only have certain frequencies. These frequencies are called resonant frequencies. Each resonant frequency is called a harmonic.
Resonance - first harmonic
- Stationary waves can only happen at resonant frequencies.
- Resonant frequencies happen when the distance between the two fixed ends is an integer multiple of half wavelengths, ½λ.
- The first resonant frequency is called the first harmonic.
- It happens when the distance between the two fixed ends is exactly ½λ.
- The first harmonic is shown in the diagram.
- It has two nodes and one antinode.
- The first harmonic is also known as the fundamental.
Second harmonic
- The second resonant frequency is called the second harmonic.
- It happens when the distance between the two fixed ends is exactly λ.
- It contains two ½λ lengths.
- The second harmonic has a frequency twice as big as the first harmonic.
- It has three nodes and two antinodes.
Third harmonic
- The third resonant frequency is called the third harmonic.
- It happens when the distance between the two fixed ends is exactly 1½λ.
- It contains three ½λ lengths.
- The third harmonic has a frequency three times as big as the first harmonic.
- It has four nodes and three antinodes.
Test yourself on Stationary Waves
Which of these statements are true of stationary waves?
When do resonant frequencies occur?