Stationary waves
8.1What the syllabus asks of you
- explain and use the principle of superposition
- show an understanding of experiments that demonstrate stationary waves using microwaves, stretched strings and air columns (it will be assumed that end corrections are negligible; knowledge of the concept of end corrections is not required)
- explain the formation of a stationary wave using a graphical method, and identify nodes and antinodes
- understand how wavelength may be determined from the positions of nodes or antinodes of a stationary wave
Read the notes first
Chapter 8: Stationary waves
Drill this topic
Every question on Stationary waves, untimed, marked as you go.
Make a worksheet
Choose the years and how many questions, then print it with the answers on separate pages.
113 questions
1May / June 2026 · Paper 11 · Q27Show mark scheme →
A1.25f
B1.50f
C1.75f
D2.00f
Mark scheme
2May / June 2026 · Paper 12 · Q28Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
3May / June 2026 · Paper 13 · Q30Show mark scheme →
A4.7 × 10⁹ Hz
B5.0 × 10⁹ Hz
C9.4 × 10⁹ Hz
D1.0 × 10¹⁰ Hz
Mark scheme
4May / June 2026 · Paper 14 · Q28Show mark scheme →
AThe resultant amplitude of the two waves at that point is equal to the sum of the amplitudes of the individual waves.
BThe resultant displacement of the two waves at that point is equal to the sum of the displacements of the individual waves.
CThe resultant frequency of the two waves at that point is equal to the sum of the frequencies of the individual waves.
DThe resultant intensity of the two waves at that point is equal to the sum of the intensities of the individual waves.
Mark scheme
5May / June 2026 · Paper 14 · Q30Show mark scheme →
Adown, down, up
Bdown, up, up
Cup, down, down
Dup, up, down
Mark scheme
6May / June 2026 · Paper 14 · Q31Show mark scheme →
Afirst higher note: 113 Hz, second higher note: 150 Hz
Bfirst higher note: 150 Hz, second higher note: 225 Hz
Cfirst higher note: 150 Hz, second higher note: 300 Hz
Dfirst higher note: 225 Hz, second higher note: 375 Hz
Mark scheme
7Oct / Nov 2025 · Paper 11 · Q29Show mark scheme →
AThey have different frequencies.
BThey have the same amplitudes.
CThey have different periods.
DThey are always in phase.
Mark scheme
8Oct / Nov 2025 · Paper 12 · Q30Show mark scheme →
Aa position where the phase difference between the two waves is always 0°
Ba position where the phase difference between the two waves is always 180°
Ca position where the stationary wave has maximum amplitude
Da position where the stationary wave has minimum amplitude
Mark scheme
9Oct / Nov 2025 · Paper 13 · Q29Show mark scheme →
AThey have different frequencies.
BThey have the same amplitudes.
CThey have different periods.
DThey are always in phase.
Mark scheme
10Oct / Nov 2025 · Paper 14 · Q29Show mark scheme →
A4
B5
C6
D9
Mark scheme
11May / June 2025 · Paper 11 · Q29Show mark scheme →
A3/2
B5/3
C5/2
D4
Mark scheme
12May / June 2025 · Paper 11 · Q31Show mark scheme →
A10 cm
B20 cm
C40 cm
D160 cm
Mark scheme
13May / June 2025 · Paper 12 · Q24Show mark scheme →
A25 MHz
B50 MHz
C2.5 GHz
D5.0 GHz
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14May / June 2025 · Paper 12 · Q30Show mark scheme →
AThey must be of the same type.
BThey must have the same period.
CThey must have the same wavelength.
DThey must travel in the same direction.
Mark scheme
15May / June 2025 · Paper 13 · Q29Show mark scheme →
Aalways
Bonly when the waves have the same amplitude
Conly when the waves travel in opposite directions
Donly when the waves have the same frequency
Mark scheme
16May / June 2025 · Paper 14 · Q25Show mark scheme →
A50 cm
B75 cm
C150 cm
D300 cm
Mark scheme
17Oct / Nov 2024 · Paper 12 · Q28Show mark scheme →
ATheir amplitudes are added together.
BTheir displacements are added together.
CTheir frequencies are added together.
DTheir velocities are added together.
Mark scheme
18Oct / Nov 2024 · Paper 12 · Q31Show mark scheme →
A1650 Hz
B2200 Hz
C3300 Hz
D6600 Hz
Mark scheme
19Oct / Nov 2024 · Paper 13 · Q28Show mark scheme →
Adouble the distance between adjacent antinodes
Bhalf the distance between adjacent nodes
Cthe distance between adjacent antinodes
Dthe distance between a node and an adjacent antinode
Mark scheme
20May / June 2024 · Paper 12 · Q23Show mark scheme →
Atime base 0.50 ms / cm
Btime base 0.50 ms / cm
Ctime base 0.50 ms / cm
Dtime base 0.50 ms / cm
Mark scheme
21May / June 2024 · Paper 12 · Q27Show mark scheme →
A1
B2
C3
D4
Mark scheme
22May / June 2024 · Paper 13 · Q27Show mark scheme →
AThey have the same amplitude.
BThey are of the same type.
CThey are transverse waves.
DThey travel in opposite directions.
Mark scheme
23Feb / March 2024 · Paper 12 · Q29Show mark scheme →
A0.40 m
B0.50 m
C0.80 m
D1.0 m
Mark scheme
24Oct / Nov 2023 · Paper 11 · Q25Show mark scheme →
AAt certain times, the string between two nodes is horizontal with all points having zero displacement.
BEach point on the string between two antinodes has an oscillation of the same amplitude.
CThe number of nodes is equal to the number of antinodes.
DTwo adjacent antinodes oscillate in phase.
Mark scheme
25Oct / Nov 2023 · Paper 11 · Q26Show mark scheme →
A4 Hz
B8 Hz
C16 Hz
D32 Hz
Mark scheme
26Oct / Nov 2023 · Paper 12 · Q25Show mark scheme →
Adiffraction
Bpolarisation
Csuperposition
Dthe Doppler effect
Mark scheme
27Oct / Nov 2023 · Paper 12 · Q26Show mark scheme →
A0.57 m
B1.1 m
C1.3 m
D1.6 m
Mark scheme
28Oct / Nov 2023 · Paper 13 · Q25Show mark scheme →
AAll the particles between two adjacent nodes oscillate in phase.
BThe amplitude of the stationary wave is equal to the amplitude of one of the waves creating it.
CThe wavelength of the stationary wave is equal to the separation of two adjacent nodes.
DThere is no displacement of a particle at an antinode at any time.
Mark scheme
29Oct / Nov 2023 · Paper 13 · Q26Show mark scheme →
A2L
B2L
CL
DL
Mark scheme
30May / June 2023 · Paper 11 · Q25Show mark scheme →
AThe waves must be coherent.
BThe waves must be of the same type.
CThe waves must be travelling in opposite directions.
DThe waves must meet in phase.
Mark scheme
31May / June 2023 · Paper 11 · Q26Show mark scheme →
A1.25f
B1.50f
C1.75f
D2.00f
Mark scheme
32May / June 2023 · Paper 12 · Q25Show mark scheme →
AThey must have a constant phase difference.
BThey must have the same frequency.
CThey must have the same wavelength.
DThey must travel at the same speed.
Mark scheme
33May / June 2023 · Paper 12 · Q26Show mark scheme →
A430 Hz
B570 Hz
C850 Hz
D1700 Hz
Mark scheme
34May / June 2023 · Paper 13 · Q25Show mark scheme →
AA short time after t0, point R on the string will be displaced.
BA short time after t0, points S and T on the string move in opposite directions.
CThe distance between P and Q is one wavelength.
DTwo moving points on the string that are equal distances from point R vibrate in phase.
Mark scheme
35May / June 2023 · Paper 13 · Q26Show mark scheme →
A1700 Hz
B2300 Hz
C3400 Hz
D6800 Hz
Mark scheme
36Feb / March 2023 · Paper 12 · Q25Show mark scheme →
A92 Hz, 138 Hz, 184 Hz, 230 Hz
B92 Hz, 184 Hz, 276 Hz, 368 Hz
C92 Hz, 276 Hz, 460 Hz, 644 Hz
D92 Hz, 276 Hz, 828 Hz, 1288 Hz
Mark scheme
37Feb / March 2023 · Paper 12 · Q26Show mark scheme →
A1
B2
C3
D4
Mark scheme
38Oct / Nov 2022 · Paper 11 · Q26Show mark scheme →
Aalways
Bonly when the waves have the same amplitude
Conly when the waves have the same frequency
Donly when the waves travel in opposite directions
Mark scheme
39Oct / Nov 2022 · Paper 11 · Q27Show mark scheme →
Agraph A
Bgraph B
Cgraph C
Dgraph D
Mark scheme
40Oct / Nov 2022 · Paper 12 · Q26Show mark scheme →
Afrequency of sound ✓, mean separation of 'quiet' spots ✓, speed of sound in air ✗
Bfrequency of sound ✓, mean separation of 'quiet' spots ✗, speed of sound in air ✓
Cfrequency of sound ✓, mean separation of 'quiet' spots ✗, speed of sound in air ✗
Dfrequency of sound ✗, mean separation of 'quiet' spots ✓, speed of sound in air ✗
Mark scheme
41Oct / Nov 2022 · Paper 12 · Q27Show mark scheme →
A+1.0 cm
B–1.0 cm
C+1.8 cm
D–1.8 cm
Mark scheme
42Oct / Nov 2022 · Paper 13 · Q25Show mark scheme →
AThe waves are longitudinal.
BThe waves are polarised.
CThe waves travel in opposite directions.
DThe waves travel in the same direction.
Mark scheme
43Oct / Nov 2022 · Paper 13 · Q26Show mark scheme →
AThe piles are where the air molecules vibrate with maximum amplitude.
BThe piles are where the air molecules vibrate with minimum amplitude.
CThe piles are where the air molecules vibrate with the highest frequency.
DThe piles are where the air molecules vibrate vertically.
Mark scheme
44May / June 2022 · Paper 11 · Q26Show mark scheme →
A16 cm
B32 cm
C48 cm
D72 cm
Mark scheme
45May / June 2022 · Paper 11 · Q27Show mark scheme →
A100 Hz
B200 Hz
C300 Hz
D500 Hz
Mark scheme
46May / June 2022 · Paper 12 · Q27Show mark scheme →
APoint R is at a node.
BPoints Q and S vibrate in phase.
CThe distance between P and T is three wavelengths.
DThe wave transfers energy from P to T.
Mark scheme
47May / June 2022 · Paper 13 · Q27Show mark scheme →
Aamplitude
Bdisplacement
Cintensity
Dwavelength
Mark scheme
48May / June 2022 · Paper 13 · Q28Show mark scheme →
A150 m s–1
B230 m s–1
C300 m s–1
D340 m s–1
Mark scheme
49Feb / March 2022 · Paper 12 · Q25Show mark scheme →
A0.040 Hz
B13 Hz
C25 Hz
D50 Hz
Mark scheme
50Oct / Nov 2021 · Paper 11 · Q23Show mark scheme →
A1.25f0
B1.50f0
C2.00f0
D3.00f0
Mark scheme
51Oct / Nov 2021 · Paper 11 · Q26Show mark scheme →
ADiagram A
BDiagram B
CDiagram C
DDiagram D
Mark scheme
52Oct / Nov 2021 · Paper 12 · Q24Show mark scheme →
A11.7 cm
B14.0 cm
C23.3 cm
D28.0 cm
Mark scheme
53Oct / Nov 2021 · Paper 12 · Q27Show mark scheme →
A333 Hz
B405 Hz
C500 Hz
D1000 Hz
Mark scheme
54Oct / Nov 2021 · Paper 13 · Q24Show mark scheme →
A425 Hz
B850 Hz
C1130 Hz
D2270 Hz
Mark scheme
55Oct / Nov 2021 · Paper 13 · Q27Show mark scheme →
AJ: -5, K: 0, L: -10
BJ: -5, K: +5, L: 0
CJ: 0, K: +5, L: +10
DJ: +5, K: -5, L: 0
Mark scheme
56May / June 2021 · Paper 11 · Q23Show mark scheme →
A4100 Hz
B5500 Hz
C8300 Hz
D11 000 Hz
Mark scheme
57May / June 2021 · Paper 11 · Q26Show mark scheme →
Aone-quarter of a wavelength
Bhalf a wavelength
Cone wavelength
Dtwo wavelengths
Mark scheme
58May / June 2021 · Paper 12 · Q26Show mark scheme →
A\frac{2L}{3}
BL
C\frac{4L}{3}
D2L
Mark scheme
59May / June 2021 · Paper 13 · Q27Show mark scheme →
AThe waves must have equal frequencies, but different speeds and wavelengths.
BThe waves must have equal speeds, but different wavelengths and frequencies.
CThe waves must have equal speeds, frequencies and wavelengths.
DThe waves must have equal wavelengths, but different speeds and frequencies.
Mark scheme
60Feb / March 2021 · Paper 12 · Q23Show mark scheme →
A\frac{2L}{9}
B\frac{2L}{8}
C\frac{4L}{9}
D\frac{4L}{8}
Mark scheme
61Feb / March 2021 · Paper 12 · Q26Show mark scheme →
A2.0 cm
B5.0 cm
C10 cm
D18 cm
Mark scheme
62Oct / Nov 2020 · Paper 11 · Q23Show mark scheme →
A2x
B4y
C2(y – x)
D4(y – x)
Mark scheme
63Oct / Nov 2020 · Paper 11 · Q26Show mark scheme →
AAll the particles between two adjacent nodes oscillate in phase.
BThe amplitude of the stationary wave is equal to the amplitude of one of the waves creating it.
CThe wavelength of the stationary wave is equal to the separation of two adjacent nodes.
DThere is no displacement of a particle at an antinode at any time.
Mark scheme
64Oct / Nov 2020 · Paper 12 · Q24Show mark scheme →
A128 Hz
B256 Hz
C384 Hz
D512 Hz
Mark scheme
65Oct / Nov 2020 · Paper 12 · Q27Show mark scheme →
A
B
C
D
Mark scheme
66Oct / Nov 2020 · Paper 13 · Q22Show mark scheme →
A1.7
B2.8
C4.0
D16
Mark scheme
67Oct / Nov 2020 · Paper 13 · Q27Show mark scheme →
A–1.0 mm
Bzero
C+0.5 mm
D+1.0 mm
Mark scheme
68May / June 2020 · Paper 11 · Q24Show mark scheme →
A220 Hz
B440 Hz
C660 Hz
D880 Hz
Mark scheme
69May / June 2020 · Paper 11 · Q27Show mark scheme →
AA short time later, point R on the string will be displaced.
BPoints S and T on the string move in opposite directions.
CThe distance between P and Q is one wavelength.
DTwo points on the string that are equal distances from point R vibrate in phase.
Mark scheme
70May / June 2020 · Paper 12 · Q24Show mark scheme →
A0.14 m
B0.28 m
C0.42 m
D0.56 m
Mark scheme
71May / June 2020 · Paper 12 · Q27Show mark scheme →
AThe waves must be coherent.
BThe waves must be of the same type.
CThe waves must be travelling in opposite directions.
DThe waves must meet in phase.
Mark scheme
72May / June 2020 · Paper 13 · Q24Show mark scheme →
A28 cm
B42 cm
C84 cm
D112 cm
Mark scheme
73May / June 2020 · Paper 13 · Q27Show mark scheme →
A[diagram A: tube with stationary wave pattern]
B[diagram B: tube with stationary wave pattern]
C[diagram C: tube with stationary wave pattern]
D[diagram D: tube with stationary wave pattern]
Mark scheme
74Feb / March 2020 · Paper 12 · Q26Show mark scheme →
A92 Hz, 138 Hz, 184 Hz, 230 Hz
B92 Hz, 184 Hz, 276 Hz, 368 Hz
C92 Hz, 276 Hz, 460 Hz, 644 Hz
D92 Hz, 276 Hz, 828 Hz, 1288 Hz
Mark scheme
75Oct / Nov 2019 · Paper 11 · Q23Show mark scheme →
Adecreases steadily
Bincreases and decreases regularly
Cincreases steadily
Dremains constant
Mark scheme
76Oct / Nov 2019 · Paper 11 · Q26Show mark scheme →
A[diagram A: two separate pulses on distance axis 5.0 m to 7.5 m]
B[diagram B: overlapping pulses forming a large central displacement on distance axis 5.0 m to 7.5 m]
C[diagram C: two overlapping pulses on distance axis 5.0 m to 7.5 m]
D[diagram D: flat rope on distance axis 5.0 m to 7.5 m]
Mark scheme
77Oct / Nov 2019 · Paper 12 · Q25Show mark scheme →
A1
B2
C3
D4
Mark scheme
78Oct / Nov 2019 · Paper 13 · Q26Show mark scheme →
Avalue of d for a maximum / cm: 46; value of d for a minimum / cm: 48
Bvalue of d for a maximum / cm: 47; value of d for a minimum / cm: 48
Cvalue of d for a maximum / cm: 48; value of d for a minimum / cm: 47
Dvalue of d for a maximum / cm: 49; value of d for a minimum / cm: 47
Mark scheme
79Oct / Nov 2019 · Paper 13 · Q28Show mark scheme →
AThe wave is longitudinal, has a wavelength of 20 cm and is stationary.
BThe wave is transverse, has a wavelength of 20 cm and is stationary.
CThe wave is transverse, has a wavelength of 40 cm and is progressive.
DThe wave is transverse, has a wavelength of 40 cm and is stationary.
Mark scheme
80May / June 2019 · Paper 11 · Q24Show mark scheme →
A16 cm
B32 cm
C64 cm
D128 cm
Mark scheme
81May / June 2019 · Paper 11 · Q27Show mark scheme →
A100 m s–1
B200 m s–1
C450 m s–1
D900 m s–1
Mark scheme
82May / June 2019 · Paper 12 · Q25Show mark scheme →
A1/2 L
BL
C2L
D4L
Mark scheme
83May / June 2019 · Paper 13 · Q26Show mark scheme →
A1.2f
B1.5f
C2.0f
D3.0f
Mark scheme
84Feb / March 2019 · Paper 12 · Q24Show mark scheme →
A\frac{7f_1}{4}
B2f_1
C4f_1
D7f_1
Mark scheme
85Feb / March 2019 · Paper 12 · Q27Show mark scheme →
Athe same amplitude and in phase
Bdifferent amplitudes and in phase
Cthe same amplitude and a phase difference of 180°
Ddifferent amplitudes and a phase difference of 180°
Mark scheme
86Oct / Nov 2018 · Paper 11 · Q26Show mark scheme →
Ablowing air over the top of an empty bottle
Bmaking a loud sound near a mountain
Cpassing monochromatic light through a double slit
Dpassing water waves through a narrow slit
Mark scheme
87Oct / Nov 2018 · Paper 12 · Q24Show mark scheme →
A430 Hz
B570 Hz
C850 Hz
D1700 Hz
Mark scheme
88Oct / Nov 2018 · Paper 12 · Q27Show mark scheme →
AP and Q
BP only
CQ only
Dneither P nor Q
Mark scheme
89Oct / Nov 2018 · Paper 13 · Q26Show mark scheme →
AAll points on the string vibrate in phase.
BAll points on the string vibrate with the same amplitude.
CPoints equidistant from N₂ vibrate with the same frequency and in phase.
DPoints equidistant from N₂ vibrate with the same frequency and the same amplitude.
Mark scheme
90May / June 2018 · Paper 11 · Q27Show mark scheme →
A100 Hz
B200 Hz
C300 Hz
D500 Hz
Mark scheme
91May / June 2018 · Paper 12 · Q24Show mark scheme →
A2L/1, 2L/2, 2L/3, 2L/4, 2L/5
B2L/2, 2L/3, 2L/4, 2L/5, 2L/6
C4L/1, 4L/2, 4L/3, 4L/4, 4L/5
D4L/1, 4L/3, 4L/5, 4L/7, 4L/9
Mark scheme
92May / June 2018 · Paper 12 · Q26Show mark scheme →
A56 Hz
B112 Hz
C5600 Hz
D11 200 Hz
Mark scheme
93May / June 2018 · Paper 12 · Q28Show mark scheme →
AGraph A
BGraph B
CGraph C
DGraph D
Mark scheme
94May / June 2018 · Paper 13 · Q24Show mark scheme →
A128 Hz
B256 Hz
C512 Hz
D1024 Hz
Mark scheme
95Feb / March 2018 · Paper 12 · Q28Show mark scheme →
Afx = fy/4
Bfx = fy/2
Cfx = 2fy
Dfx = 4fy
Mark scheme
96Oct / Nov 2017 · Paper 11 · Q23Show mark scheme →
A2x
B4y
C2(y – x)
D4(y – x)
Mark scheme
97Oct / Nov 2017 · Paper 11 · Q27Show mark scheme →
A[diagram A]
B[diagram B]
C[diagram C]
D[diagram D]
Mark scheme
98Oct / Nov 2017 · Paper 12 · Q24Show mark scheme →
A128 Hz
B256 Hz
C384 Hz
D512 Hz
Mark scheme
99Oct / Nov 2017 · Paper 12 · Q27Show mark scheme →
A5.0 cm
B6.0 cm
C10.0 cm
D12.0 cm
Mark scheme
100May / June 2017 · Paper 11 · Q27Show mark scheme →
A\frac{f}{4}
B\frac{f}{2}
C2f
D4f
Mark scheme
101May / June 2017 · Paper 12 · Q27Show mark scheme →
Aphase difference: 90°; amplitude: different
Bphase difference: 90°; amplitude: same
Cphase difference: 180°; amplitude: different
Dphase difference: 180°; amplitude: same
Mark scheme
102May / June 2017 · Paper 13 · Q26Show mark scheme →
A50 cm
B75 cm
C150 cm
D300 cm
Mark scheme
103Feb / March 2017 · Paper 12 · Q27Show mark scheme →
A–1
B0
C1
D2
Mark scheme
104Oct / Nov 2016 · Paper 11 · Q24Show mark scheme →
A0.14 m
B0.28 m
C0.42 m
D0.56 m
Mark scheme
105Oct / Nov 2016 · Paper 11 · Q28Show mark scheme →
A0
B45°
C90°
D135°
Mark scheme
106Oct / Nov 2016 · Paper 12 · Q26Show mark scheme →
A–1.0 mm
Bzero
C+0.5 mm
D+1.0 mm
Mark scheme
107Oct / Nov 2016 · Paper 12 · Q29Show mark scheme →
A1.0 × 10^8 Hz
B2.0 × 10^8 Hz
C1.0 × 10^10 Hz
D2.0 × 10^10 Hz
Mark scheme
108Oct / Nov 2016 · Paper 13 · Q24Show mark scheme →
A0.14 m
B0.28 m
C0.42 m
D0.56 m
Mark scheme
109Oct / Nov 2016 · Paper 13 · Q28Show mark scheme →
A0
B45°
C90°
D135°
Mark scheme
110May / June 2016 · Paper 11 · Q24Show mark scheme →
AAll the particles between two successive nodes oscillate in phase.
BThe amplitude of the stationary wave is equal to the amplitude of one of the waves creating it.
CThe wavelength of the stationary wave is equal to the separation of two adjacent nodes.
DThere is no displacement of a particle at an antinode at any time.
Mark scheme
111May / June 2016 · Paper 12 · Q25Show mark scheme →
A0
BA
C2A
D4A
Mark scheme
112Feb / March 2016 · Paper 12 · Q24Show mark scheme →
AAn antinode is formed at the surface of the metal sheet.
BA node is a quarter of a wavelength from an adjacent antinode.
CThe oscillations at X are in phase with those at Y.
DThe air particles oscillate perpendicular to the line WZ.
Mark scheme
113Feb / March 2016 · Paper 12 · Q25Show mark scheme →
A92 Hz, 138 Hz, 184 Hz, 230 Hz, 276 Hz
B92 Hz, 184 Hz, 276 Hz, 368 Hz, 460 Hz
C92 Hz, 276 Hz, 460 Hz, 644 Hz, 828 Hz
D92 Hz, 276 Hz, 828 Hz, 2484 Hz, 7452 Hz
Mark scheme