Superposition and stationary waves Cambridge International AS & A Level Physics revision
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In plain words
When two waves meet they simply add. Send a wave down a string and let it reflect back on itself, and at certain frequencies the two combine into a pattern that doesn't seem to travel at all: some points never move, others swing wildly. That is a stationary wave, and it is how every musical instrument works.
4 things to know
- Superposition: where waves meet, the resultant displacement is the sum of their individual displacements.
- A stationary wave forms when two waves of the same frequency travelling in opposite directions superpose, usually a wave and its own reflection. Nodes are points of zero amplitude; antinodes are points of maximum amplitude. Neighbouring nodes are half a wavelength apart.
- A stretched string fixed at both ends has a node at each end. Its simplest mode is a single loop, so the string's length is half a wavelength. The next modes have two, three ... loops, at two, three ... times the frequency.
- All the points between two neighbouring nodes oscillate in phase. A stationary wave does not transfer energy along the string.
Worked example
A string 0.80 m long is fixed at both ends, and waves travel along it at 240 m/s. Find the frequency of its simplest mode.
- In the simplest mode the string holds half a wavelength: λ = 2 × 0.80 = 1.6 m.
- f = v ÷ λ = 240 ÷ 1.6.
- = 150 Hz.
Tips and tricks
- To find a wavelength, measure across several nodes: the distance from the first node to the fifth is two whole wavelengths.
- Node to the next antinode is a quarter of a wavelength, not a half.
It lands in your notebook with its questions as flashcards.
Superposition and stationary waves: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the distance between two neighbouring nodes?
And from a node to the next antinode is a quarter.
What is the amplitude at a node?
The two waves always cancel there.
How is a stationary wave formed?
Usually a wave and its own reflection.
A string of length L is fixed at both ends. What is the wavelength of its simplest mode?
The string holds half a wavelength.
What does a stationary wave not do?
The energy stays in the pattern.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Superposition and stationary waves
Cambridge International AS & A Level Physics 9702 · 6 marks · papermunch.org
Name ______________________________ Date ______________
State two differences between a stationary wave and a progressive wave.[2]
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Any two: a stationary wave does not transfer energy, a progressive wave does; a stationary wave has nodes and antinodes, so the amplitude varies from point to point, whereas every point on a progressive wave has the same amplitude; points between two nodes are all in phase, whereas the phase changes steadily along a progressive wave.
The distance between neighbouring nodes on a stationary wave is 0.25 m. Find the wavelength.[2]
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0.50 m.
The simplest mode of a string has a frequency of 100 Hz. Find the frequencies of the next two modes.[2]
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200 Hz and 300 Hz.
Answers: Superposition and stationary waves
- 1. Any two: a stationary wave does not transfer energy, a progressive wave does; a stationary wave has nodes and antinodes, so the amplitude varies from point to point, whereas every point on a progressive wave has the same amplitude; points between two nodes are all in phase, whereas the phase changes steadily along a progressive wave.
- 2. 0.50 m.
- 3. 200 Hz and 300 Hz.