AQA A-level Physics 7408 · Paper 1 · Spec 3.3.1
Progressive and Stationary Waves
See the particles of a wave oscillate, build a stationary wave from two travelling waves, and run required practical 1 on a virtual string. Free simulations, exam questions and a printable booklet.
On this page: ● node (N), ○ antinode (A) · — wave travelling right · - - wave travelling left
What is moving in a wave?
The wave moves along, but each particle only oscillates about its own rest position. Switch between a transverse and a longitudinal wave, and compare particles P and Q. The graph on the right follows P and Q over time.
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More particles per metre means more mass per metre, μ, so with the same tension the wave is slower: c = √Tμ. The wavelength then follows from λ = cf. Displacements are drawn larger than scale so you can see them. The wave travels to the right. In the longitudinal view a displacement to the right counts as positive on the graph.
Polarisation: evidence that a wave is transverse
A polarising filter only lets through oscillations in one plane. Turn the second filter, the receiving aerial or the slotted screen, and see which waves are affected.
Brightness and signal are shown in words and a bar, not numbers: AQA does not ask you to calculate how much light gets through at an angle.
Building a stationary wave
A wave travelling right meets its reflection travelling left. They have the same frequency and amplitude, and they superpose. Step through one period in eighths and watch the nodes stay still.
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String lab: required practical 1
A vibration generator drives a string over a pulley, with masses hanging from the end. Turn the signal generator until the string resonates, then record the reading. Change one variable at a time and plot a straight-line graph.
| l / m | T / N | μ / kg m−1 | n | f / Hz | f1 / Hz |
|---|
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g = 9.81 N kg−1. The generator end of the string is very nearly a node, because the vibration generator moves only a tiny amount. Safety in the real practical: keep your feet clear of the hanging masses and wear eye protection in case the wire snaps.
Key equations for progressive and stationary waves
Quick catch
Three rounds of five multiple-choice questions, each round harder than the last. Pick A, B, C or D and the reasons appear straight away. Get 4 of 5 right to unlock the next round.
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Where it comes from
Three ideas behind stationary waves, built up step by step. AQA expects the graphical explanation and the harmonics; the third tab shows the algebra behind them.
Test yourself
35 exam-style questions in three levels: Core, Exam-style and Stretch for A*. Each level shows a few at a time. Press Try another question for a different one. Type numbers without units. For the explain parts, write your answer, then mark it against the mark scheme.
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Download the booklet
Notes, worked examples, equation cards, 17 quick checks and 32 exam-style questions on progressive and stationary waves, including required practical 1, to print and write on. The answers are at the back.
Progressive and Stationary Waves: notes and practice booklet
Print it, write in the spaces, then check your answers at the back.
It opens in a new tab. Use the download or print button in the PDF viewer to keep a copy. Print it double-sided and write in the spaces. In the PDF, each question links to its answer and back again.
Teachers: free for classroom use. Please share this page link rather than the file, so students always get the latest version.
Progressive and stationary waves: common questions
Why is the first-harmonic wavelength twice the length of the string?
Both ends are clamped, so both must be nodes. The simplest pattern between two nodes is a single loop, and one loop is half a wavelength.
A guitar string 0.65 m long therefore has a first-harmonic wavelength of 1.30 m. The next harmonics have two and three loops, with λ = l and 2l3.
Exam trap. Using λ = l for the first harmonic halves every wave speed and frequency you calculate.
Do stationary waves carry energy?
A stationary wave stores energy, but it transfers no net energy along the string. It is made of two equal waves travelling in opposite directions, so their energy flows cancel.
Inside each loop, energy moves back and forth between kinetic energy (when the string is flat and moving fastest) and potential energy in the stretched string (at the extremes). Nodes never move, so energy cannot cross them.
Exam trap. In a comparison table, write “no net energy transfer” for the stationary wave, not just “no energy”.
Why can’t sound be polarised?
Polarising a wave means restricting its oscillations to one plane. That needs oscillations at right angles to the direction of travel, which only transverse waves have.
Sound is longitudinal: the air oscillates back and forth along the direction the sound travels. There is no sideways oscillation to restrict, so a slotted screen or filter changes nothing however you turn it. Try the third mode of the polarisation simulation.
Exam trap. “Only transverse waves can be polarised” earns the mark; “sound is a different type of wave” does not.
Why do Polaroid sunglasses cut glare?
Light reflected from water, wet roads and car bonnets is partly plane polarised, with its oscillations mostly horizontal. The sunglasses contain Polaroid with its transmission axis vertical.
The vertical Polaroid blocks much of the horizontally polarised glare, while still letting through about half of the unpolarised light from everything else. Tilt your head 90° with the sunglasses on and the glare comes back.
Exam trap. Say which direction the reflected light is polarised in and which way the filter is aligned: “at right angles” is the key idea.