The long-answer questions in this topic come in a few types, and each type gets marked against the same points every time. Choose one, learn its chain, then fill in the details from the question.
OCR students: these questions come from Edexcel papers, but every bit of the physics is on the OCR A spec too. OCR’s own 6-mark questions are the ones marked with an asterisk (*), and they are marked the same way: by how complete and well linked your explanation is.
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Print it out
The notes: both chains, how to mark up a question and every worked answer. Or just the questions, with the chains at the top and the answers at the back.
“Explain how a standing (stationary) wave is set up…”
…or a question about nodes or antinodes, or waves that reflect back to where they came from. And the biggest clue of all: a musical instrument.
Watch out for structures that oscillate dangerously too, like a bridge, a tall chimney or a cable in the wind. The wind sets up waves that travel along the structure and reflect off its fixed ends, so a standing wave forms on the structure itself.
Every musical instrument makes its note with a standing wave. So if the question shows an instrument, start thinking “standing wave” straight away. The wave travels along the string or the air inside the pipe, reflects at the end, and comes back on itself.
🎸Strings
Guitar, violin, harp, piano. The wave reflects at the two fixed ends of the string (the bridge and the nut on a guitar).
🎺Pipes
Organ, flute, recorder, trumpet. The air column inside vibrates, and the sound wave reflects at the ends of the pipe.
🥁Drums
The stretched skin vibrates. The wave reflects at the fixed rim, giving a standing wave in two dimensions.
Only certain frequencies fit a whole number of loops between the ends. That’s why each string or pipe plays its own note.
Standing wave
Interference pattern
The waves
Two coherent waves on the same line, travelling in opposite directions. One is usually the reflection of the other
Waves from two or more coherent sources (or two paths) meeting at a point
Clue words
string, pipe, instrument, reflected back, a bridge or structure in the wind, nodes, antinodes
two slits, two speakers, bright and dark lines, louder and quieter places, path difference
What you see
Nodes and antinodes at fixed places, half a wavelength apart
Maxima and minima, set by the path difference to each point
Both need coherent waves: the same frequency and a constant phase difference. That keeps the nodes and antinodes (or the maxima and minima) in the same places, so you get a steady pattern.
Both use superposition, so the mark schemes overlap. The difference is where the two waves come from: one wave and its own reflection (standing wave), or two separate sources ().
2. The standing wave chain: six links, six marks
THE STANDING WAVE CHAIN reflect → superpose
Two waves first, then where the nodes and antinodes form
Say it until it sticks: opposite directions · superpose · in phase · antiphase · nodes and antinodes form · min and max
1
Two waves, opposite directionsThe wave reflects at the end, so two coherent waves travel in opposite directions.
2
SuperposeWhere they meet, the two waves superpose (interfere).
3
In phase → constructiveWhere the waves are in phase (path difference nλ), they interfere constructively.
4
Antiphase → destructiveWhere the waves are in antiphase (path difference (n + ½)λ), they interfere destructively.
5
Nodes and antinodes formNodes form at the points of destructive interference; antinodes at the points of constructive interference.
6
Min and maxNodes are points of minimum (zero) amplitude; antinodes are points of maximum amplitude.
The trap: the result without the reason. “The waves cancel out to make nodes” misses two marks. Say why (the waves are in antiphase) and what kind of interference (destructive). The same goes for the antinodes: in phase, constructive.
No spare link this time. The guitar mark scheme has exactly six points for six marks, so you need every link. Nodes and antinodes are easy to swap over: a Node has No movement.
3. Before you write: mark up the question
Ring two things and underline the trigger. The question doesn’t always say where the wave reflects: if it doesn’t, you supply it.
Ring · VWhat vibrates
The string, the air in the pipe, the air between the loudspeaker and the board.
Ring · RWhere it reflects
The fixed ends of the string, the end of the pipe, the fixed ends of a bridge or cable.
UnderlineThe trigger
“standing wave”, “stationary wave”, a musical instrument, nodes or antinodes, a structure oscillating in the wind.
If the question shows…
What vibrates
Where it reflects (link 1)
a stringed instrument (guitar, violin, harp)
The string
The two fixed ends of the string
a wind instrument or pipe (organ, flute, tube)
The air column
The ends of the pipe
a structure in the wind (bridge, tall chimney, cable)
The structure itself
Its fixed ends
4. Worked example: the guitar
A standing wave on a guitar stringEdexcel A Level Physics past paper · 6 marks
The photograph shows a guitar. The strings of the guitar are at the same tension.
The first harmonic: the note you hear. The wave reflects at both fixed ends and the two coherent waves superpose: a node (N) at each end, where they are in antiphase, and an antinode (A) in the middle, where they are in phase.
When a stringV is plucked, a standing wave is set up on the string.
(a) * Explain how a standing wave is set up on a string. (6)
The trigger“standing wave”, and a musical instrument. Run the standing wave chain.
Vibrates and reflectsV = the string. R isn’t in the question, so you add it: the wave reflects at the fixed ends (the bridge and the nut).
Six marks
the * means your writing is marked too
six marks, six links: none spare
Your turn Have a go before you look
Your answer stays on this device, so you can come back to it.
Step 1 Run the chain in note form
1reflects at fixed ends: 2 coherent waves, opposite directions2superpose3in phase → constructive4antiphase → destructive5nodes at destructive, antinodes at constructive6node = min amplitude, antinode = max
Step 2 Write it in full sentences
1When the string is plucked, a wave travels along the string and reflects at the fixed ends, so there are two coherent waves travelling in opposite directions along the string.✓ 1 mark
2Where the two coherent waves meet, they superpose (interfere).✓ 1 mark
3At points where the two waves are in phase (path difference nλ), there is constructive interference.✓ 1 mark
4At points where the two waves are in antiphase (path difference (n + ½)λ), there is destructive interference.✓ 1 mark
5Nodes form at the points of destructive interference, and antinodes form at the points of constructive interference.✓ 1 mark
6Nodes are points of minimum (zero) amplitude, and antinodes are points of maximum amplitude. The fixed ends are always nodes.✓ 1 mark
Six marking points, six marks available: every link earns its mark.
Check it against the mark scheme
Mark scheme says
Link
Two waves travelling in opposite directions
1
(1)
Superpose / interfere
2
(1)
Constructive (interference) if waves in phase, or if path difference = nλ
3
(1)
Destructive (interference) if waves in antiphase, or if path difference = (n + ½)λ
4
(1)
Nodes are formed from points of destructive (interference) or antinodes are formed from points of constructive (interference)
5
(1)
Nodes are points with min amplitude and antinodes are points with max amplitude
6
(1)
6 marks. Indicative content, so quality of written communication counts: write it in order, and the chain does that for you. Always say the waves are coherent (same frequency, constant phase difference): that word earns credit, “the same frequency” on its own doesn’t.
5. Your turn: practise the chain
Same chain, different set-ups. Mark up the question first (ring what vibrates, ring where it reflects, underline the trigger), write your answer, then open the answer to see the mark-up, the chain and the mark scheme.
Practice 1 · The Aeolian harpEdexcel A Level Physics past paper · 2 marks
An Aeolian harp is a stringed musical instrument that is ‘played’ by the wind.
Each string is fixed at both ends, like a guitar string. The wind blows at right angles to the strings and makes them vibrate; the waves reflect at the fixed ends. The middle string shows its first harmonic.
As air passes the stringsV, it forces them to vibrate, creating stationary waves on the strings.
(a) Explain how stationary waves are formed on the strings. (2)
The trigger“stationary waves”, and “musical instrument”. Standing wave chain.
Vibrates and reflectsV = the strings. R = the fixed ends of each string (not in the question: you add it).
Two marks
two marks = links 1 and 2
the first two links are always the same
Your turn Write your answer
Your answer stays on this device.
Step 1 Run the chain in note form
1reflects at fixed ends: 2 coherent waves, opposite directions2superpose2 marks: stop here
Step 2 Write it in full sentences
1Waves travel along each string and reflect at the fixed ends, so there are two coherent waves travelling in opposite directions along the string.✓ 1 mark
2The two waves superpose (interfere), producing nodes and antinodes: a stationary wave.✓ 1 mark
Two marks, two links. Writing links 3–6 won’t lose marks, but it costs time you need for the rest of the paper.
Check it against the mark scheme
Mark scheme says
Link
(Two) waves travelling in opposite directions, or wave reflected back on itself
1
(1)
Superposition / interference occurs
2
(1)
2 marks. Always say the waves are coherent (same frequency, constant phase difference): that word earns credit, “the same frequency” on its own doesn’t.
Practice 2 · Loudspeaker and reflecting boardEdexcel A Level Physics past paper · 3 marks
(c) An alternative method to determine a value for the speed of sound is shown in the diagram.
A and B are both nodes. Near the loudspeaker the reflected wave has travelled much further than the wave from the speaker, so it is much weaker.
A loudspeaker is placed at a distance from a vertical reflecting boardR. Sound wavesV reflect off the board and set up a standing wave between the loudspeaker and the board. A microphone connected to a sound meter is moved in a straight line from the loudspeaker to the board.
As the microphone is moved, the sound meter records the varying intensity of the standing wave. The sketch graph shows how the intensity varies with distance from the loudspeaker.
(i) Explain why the intensity at point B is less than the intensity at point A. (3)
The trigger“standing wave”. Loudspeakers usually mean interference, but here the sound reflects back off the board: one wave and its own reflection. Use links 4 and 5: A and B are nodes.
Vibrates and reflectsV = the sound waves (the air). R = the reflecting board.
The extra idea
amplitude falls with distance travelled
at B both waves have travelled about the same distance
Your turn Write your answer
Your answer stays on this device.
Step 1 Run the chain in note form
1A and B are nodes: antiphase, destructive2amplitude falls with distance travelled3at A: very different amplitudes4at B: similar distances, similar amplitudes5B cancels more: lower intensity
Step 2 Write it in full sentences
1A and B are both nodes, where the wave from the loudspeaker and its reflection (two coherent waves) are in antiphase and interfere destructively.✓ 1 mark
2The amplitude (and intensity) of the sound decreases with the distance travelled.✓ 1 mark
3At A, the wave from the loudspeaker has travelled only a short distance but the reflected wave has travelled much further, so their amplitudes are very different and they only partly cancel.goes with 4
4At B, near the board, the two waves have travelled similar distances, so they have similar amplitudes.✓ 1 mark
5So at B the waves cancel almost completely, and the intensity is lower than at A.answers the question
The answer isn’t “B is further away so it’s quieter”. It’s about how well the two waves cancel.
Check it against the mark scheme
Mark scheme says
Link
Amplitude/energy/intensity of the sound wave reduces with distance travelled
2
(1)
Appreciate that at A or B two waves are interfering destructively, or at A and B there are nodes
1
(1)
At B the waves have travelled similar distances so have similar amplitudes
4
(1)
See it move.The stationary waves lesson has an animation you can pause: watch the two waves superpose into nodes and antinodes.
“Explain why there is a bright line / a quiet spot / colours…”
…with waves arriving at a point from two or more coherent sources, or by two different paths: two slits, two loudspeakers, sound bouncing off the walls of a hall, light scattering off the tracks of a CD. Some places get a maximum (bright, loud) and some a minimum (dark, quiet).
Not a standing wave? A standing wave is one wave and its own reflection travelling in opposite directions along the same line. Here, the waves come from separate sources and meet at a point. If you’re asked about positions in a room or on a screen, think interference. (.)
2. The interference chain: six links
THE INTERFERENCE CHAIN sources → path difference
Where the waves come from, then how far each one travels
Say it until it sticks: two sources · superpose · path difference · nλ constructive · (n + ½)λ destructive · so…
1
Two sourcesWaves reach the point from two (or more) coherent sources (same frequency, constant phase difference), or by different paths. Name them from the question.
2
SuperposeAt the point, the waves superpose (interfere).
3
Path differenceThe waves travel different distances, so there is a path difference, and so a phase difference.
4
nλ → constructive BRIGHT / LOUDPath difference a whole number of wavelengths (phase difference 0, 2π…): in phase, constructive interference, maximum.
5
(n + ½)λ → destructive DARK / QUIETPath difference an odd number of half wavelengths (phase difference π, 3π…): antiphase, destructive interference, minimum.
6
So…Link it back to the question: the bright line, the quiet seat, the colours.
The trap: mixing up path and phase. Path difference is a distance (in wavelengths); phase difference is an angle (in radians). “A path difference of π” scores nothing. Keep the pairs together: nλ ↔ 0, 2π, 4π and (n + ½)λ ↔ π, 3π, 5π.
Use the chain for part questions too. A 3-mark “why is it bright here?” is links 3, 4 and 6. The longer questions want the whole chain, plus whatever extra the question asks for, like a fix for the problem.
3. Before you write: mark up the question
Ring the sources and the point, underline what happens there. The sources aren’t always named: reflections off walls count as sources too.
Ring · SThe sources
Two slits, two speakers, the walls that reflect, the tracks of a CD.
Ring · PThe point
Where the waves meet: O or P on a screen, a seat in the audience, your eye.
UnderlineWhat happens there
Bright or dark, loud or quiet, colours. That tells you which link (4 or 5) you need.
If the question says it’s…
Path difference
So your answer says
bright, loud, a maximum
nλ (phase difference 0, 2π…)
In phase, constructive interference
dark, quiet, a minimum
(n + ½)λ (phase difference π, 3π…)
Antiphase, destructive interference
coloured, from white light
nλ happens at a different angle for each wavelength
Each wavelength has constructive interference at a different angle, so a spectrum
4. Worked example: two slits
The bright lines from two slitsEdexcel A Level Physics past paper · 4 marks
The experiment was carried out with laser light of wavelength 600 nm. The diagram below shows two paths taken by the light after it has passed through the two slits A and BS. The diagram is not to scale.
To O the two paths are the same length. To P, AP is one wavelength longer than BP (the gold bit).
(i) Point OP is a point equidistant from the two slits. Explain why there is a bright line at this point. (3)
(ii) The next bright line is observed on the screen at point P. Lines AP and BP show the path of the light from each slit to the screen at P. State the difference in the lengths of the paths AP and BP. (1)
The clue“equidistant” and “difference in the lengths of the paths”: this is all about path difference.
Sources and pointS = the two slits A and B. P = point O, then point P.
What happens there
“bright line” = constructive, link 4
“next bright line” = n = 1
Your turn Have a go before you look
Your answer stays on this device, so you can come back to it.
Step 1 Run the chain in note form
12 coherent sources: slits A and B2superpose at O3equidistant: path difference 04in phase → constructive6maximum intensity: bright line(ii) next bright line: n = 1, so λ
Step 2 Write it in full sentences
(i)
1Light from the two slits is coherent, and the waves superpose at O.sets it up
2O is equidistant from the slits, so the path lengths AO and BO are equal: the path difference is zero.✓ 1 mark
3So the waves arrive in phase (phase difference zero).✓ 1 mark
4They undergo constructive interference, giving maximum intensity: a bright line.✓ 1 mark
(ii)
5P is the next bright line, so the path difference is one wavelength: AP − BP = 600 nm (6.0 × 10−7 m).✓ 1 mark
For (ii) give the number. “nλ” on its own scores nothing: the mark scheme says so.
Check it against the mark scheme
Mark scheme says
Link
(i) Path lengths (A–O and B–O) are equal, or path difference is zero
2
(1)
(i) Will arrive in phase, or phase difference is zero
3
(1)
(i) (Bright line is position of) constructive interference/superposition
4
(1)
(ii) 600 nm, or 600 × 10−9 m, or 6.0 × 10−7 m, or one wavelength, or λ. Do not accept nλ
5
(1)
4 marks. “Constructive” needs underlining in your head: it’s the word the mark is for. Always say the waves are coherent (same frequency, constant phase difference): that word earns credit, “the same frequency” on its own doesn’t.
5. Your turn: practise the chain
Same chain, harder set-ups. Ring the sources, ring the point, underline what happens there, then write your answer before you open it.
Practice 1 · The pipe organ in a concert hallEdexcel A Level Physics past paper · 6 marks
* The photograph shows a pipe organ in a concert hall.
Sound reaches the listener by several paths of different lengths. The walls and ceiling act like extra sources.
When the organ is played, sound travels through the air to a person in the audienceP as a wave. It is found that there are some positions in the concert hall where particular frequencies are quieter than others.
Explain why this might be the case and give an action that could be taken to eliminate this problem. (6)
Two jobsExplain it with the interference chain, then give an action. The action is a mark of its own.
Sources and pointS isn’t named: it’s the organ and the walls and ceiling that reflect the sound. P = the person in the audience.
What happens there
“quieter” = destructive, link 5
other frequencies louder = constructive, link 4
Your turn Write your answer
Your answer stays on this device.
Step 1 Run the chain in note form
1reflect off walls: waves arrive by different paths2superpose3some frequencies: (n + ½)λ, odd multiple of π4destructive → quieter5others: nλ, 0 or 2π6constructive → louder7absorbing material on walls
Step 2 Write it in full sentences
1Sound waves from the organ reflect off the walls, ceiling and other surfaces, so coherent waves reach a listener by different paths.✓ 1 mark
2The waves arriving from different directions superpose at the listener.goes with 3
3For some frequencies the path difference is an odd number of half wavelengths, so the waves arrive with a phase difference of an odd multiple of π (antiphase).✓ 1 mark
4They interfere destructively, so those frequencies are quieter.✓ 1 mark
5For other frequencies the path difference is a whole number of wavelengths (phase difference zero or a multiple of 2π), so the waves arrive in phase.✓ 1 mark
6They interfere constructively, so those frequencies are louder.✓ 1 mark
7The problem comes from reflections, so cover the walls and ceiling with sound-absorbing material (soft panels, curtains) to reduce the reflections.✓ 1 mark
Why only some frequencies? At one seat the path difference is fixed, but the wavelength depends on the frequency. So whether the path difference comes out as nλ or (n + ½)λ depends on the frequency.
Check it against the mark scheme
Mark scheme says
Link
Sound waves incident upon surfaces within the concert hall will be reflected
1
(1)
Some frequencies arrive from different directions with a phase difference of (any odd multiple of) π radians, or path difference is an odd number of half wavelengths
2–3
(1)
Destructive superposition/interference will occur, causing the waves with those frequencies to be quieter than others
4
(1)
Other frequencies arrive with a phase difference of zero or (any multiple of) 2π radians, or a whole number of wavelengths
5
(1)
Constructive superposition/interference will occur, causing waves with those frequencies to be louder than others
6
(1)
Problem arises due to reflections from walls, so use absorbing material on surfaces to reduce reflections
7
(1)
Indicative content, so your writing is marked too. The organ pipes make their notes with standing waves, but this question is about the hall: that’s interference. Always say the waves are coherent (same frequency, constant phase difference): that word earns credit, “the same frequency” on its own doesn’t.
Practice 2 · Colours from a CDEdexcel A Level Physics past paper · 6 marks
* The light from a lamp is reflected from the surface of a CD, which consists of a spiral track of elongated bumpsS.
Each track scatters light in all directions. Light from many tracks superposes, and each wavelength has constructive interference at its own angle.
A physics student notices that although the light from the lamp is white, different colours are seen in the reflected light. He suggests that the colours are produced when diffraction occurs at the surface of the CD.
Discuss the extent to which the student’s suggestion explains the presence of colours in the light reflected from the surface of the CD. (6)
“Discuss the extent”Is the student right, and is it the whole story? Diffraction is only half of it: you need interference too.
Sources and pointS = every bit of the track: each one scatters light, so there are many sources. P = the eye looking at the CD.
What happens there
“white” = a mix of wavelengths
“colours” = each wavelength has constructive interference at a different angle
Your turn Write your answer
Your answer stays on this device.
Step 1 Run the chain in note form
1yes, diffraction at the CD surface2each ring = a source, scatters in all directions3superpose: interference4nλ (even multiple of π) → constructive5white light = range of λ6each λ constructive at a different angle: spectrum
Step 2 Write it in full sentences
1The student is partly right: diffraction does occur when light is reflected from the CD surface.✓ 1 mark
2Each ring of the track acts as a source, diffracting (scattering) the light in all directions.✓ 1 mark
3The coherent light from the many rings superposes, so interference occurs.✓ 1 mark
4In directions where the path difference is a whole number of wavelengths (phase difference an even multiple of π), the waves are in phase and interfere constructively (reinforce).✓ 1 mark
5White light is a mixture of wavelengths.✓ 1 mark
6So each wavelength has constructive interference at a different angle, separating the colours into a spectrum.✓ 1 mark
7So diffraction on its own doesn’t explain the colours: it’s diffraction followed by interference, just as in a diffraction grating.answers “discuss”
“Discuss the extent” wants a verdict. Start by saying how far the student is right, and finish by saying what’s missing.
Check it against the mark scheme
Mark scheme says
Link
Analyses and interprets the text to conclude that diffraction occurs when light is reflected from the CD surface
1
(1)
Each ring on the CD acts as a diffraction centre scattering light in all directions
2
(1)
Interference occurs (superposition of light from the multiple light sources)
3
(1)
In directions with a phase difference equal to an even multiple of π rad, or a path difference equal to a whole number of wavelengths, constructive interference (reinforcement) occurs
4
(1)
White light is a range (mixture) of wavelengths
5
(1)
Hence each wavelength of light reinforces in a different direction, which explains why a spectrum is seen
6
(1)
6 marks, indicative content. Same chain as the organ, plus links 5 and 6 for the colours. Always say the waves are coherent (same frequency, constant phase difference): that word earns credit, “the same frequency” on its own doesn’t.
Learn the words the mark scheme uses.Coherent, path difference, phase difference, superposition: all the Module 4 waves and quantum definitions, with wall posters.
