AQA A-Level Physics Paper 1, June 2024: Question 7
7 marks · Medium difficulty · Extended Answer
Analyze stationary waves on a string by determining progressive wave amplitude, wave speed, phase relationship, and sketching displacement-time graphs for a specific point.
Practise this questionQuestion
Question text
07 An experiment is done to investigate stationary waves on a string.
A string of length 1.05 m is attached between a clamp stand and a vibration
generator. A stationary wave is formed on the string when the vibration generator
frequency is 625 Hz.
Figure 6 shows the variation of displacement with distance from one end of the string
at time t = 0
At this time all points on the string have their maximum displacement.
S is one point on the string.
Figure 6
The stationary wave is produced by two progressive waves travelling in opposite
directions on the string.
07.1 Deduce the amplitude of one of the progressive waves.
[1 mark]
17 amplitude = mm
07.2 Determine, in m s−1, the speed of one of the progressive waves.
[2 marks]
speed = m s−1
07.3 State the phase relationship between the two waves when t = 0
[1 mark]
07.4 Sketch, on Figure 7, a graph to show how the displacement of S varies with t.
[3 marks]
Figure 7
END OF SECTION A
Section B
Each of Questions 08 to 32 is followed by four responses, A, B, C and D.
For each question select the best response.
Only one answer per question is allowed.
For each question, completely fill in the circle alongside the appropriate answer.
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Mark scheme
Show the mark scheme
Question Answers Additional comments/Guidelines Mark AO
07.1 3.5 mm Accept 3.4 to 3.6 1 AO3
07.2 Evidence of use of v = f λ including 625 (Hz) Allow range of 0.68 – 0.72 m in λ 2 AO3
Uses wavelength = 0.7 m to get 440 (m s–1) or 425-450 m s-1
07.3 In phase OR 0 Accept 2π, 360o and multiples 1 AO1
07.4 Sinusoidal wave starting at displacement = 4 mm Tolerance on drawing: half a square 3 AO3
Amplitude = 4 mm
Period (= 625–1) = 1.6 ms
Judge shape of wave on their first complete
cycle.
If there is no complete cycle, the line they
have drawn must cover the width of the grid.
Total 7
How to answer it
Investigating Stationary Waves on a String
What this question tests
This question assesses your understanding of stationary (standing) waves formed by the superposition of two progressive waves travelling in opposite directions. Key skills include interpreting displacement-distance and displacement-time graphs, applying wave equations ( v = fλ ), determining progressive wave amplitudes from standing wave profiles, and sketching simple harmonic motion behaviours over time.
Part (a): Amplitude of a Progressive Wave
Deduce the amplitude of one of the progressive waves.
✅ Correct Answer
3.5 mm (Acceptable range: 3.4 to 3.6 mm )
💡 Key Knowledge
- A stationary wave is formed by two progressive waves of equal amplitude and frequency travelling in opposite directions.
- The maximum displacement of a stationary wave (the antinode) is equal to 2 × A , where A is the amplitude of each individual progressive wave.
❌ Common Errors
Students often incorrectly state the full antinode displacement ( 7.0 mm ) as the amplitude of the progressive wave, forgetting that amplitudes constructively interfere to double the height.
Part (b): Speed of the Progressive Waves
Determine, in m s⁻¹, the speed of the progressive waves.
✅ Correct Answer
440 m s⁻¹ (Acceptable range: 425 to 450 m s⁻¹ based on λ = 0.70 m)
📐 Calculation Steps
- Find Wavelength (λ): From Figure 6, look at the spatial profile. Two full loops span from x = 0 to x = 1.05 m? Let's check: one loop is half a wavelength (λ/2). Looking at the graph, a full wavelength spans 0.70 m (from x = 0 to x = 0.7 shows one full wave cycle, or read distance for 1.5 wavelengths = 1.05 m, so λ = 1.05 / 1.5 = 0.70 m).
- Apply Wave Equation: v = fλ
- Substitute values: v = 625 Hz × 0.70 m = 437.5 m s⁻¹ (rounds to 440 m s⁻¹ to 2 sig figs matching given data).
🧠 Exam Technique & Marking
Mark 1: Evidence of using v = fλ along with the frequency 625 Hz .
Mark 2: Correct substitution of wavelength ( 0.70 m ) leading to the final speed.
Part (c): Phase Relationship
State the phase relationship between the two waves when t = 0.
✅ Correct Answer
In phase (or 0 , 2π , 360° and multiples)
💡 Key Knowledge
At points of maximum displacement (antinodes) when t = 0 , the two constituent progressive waves arrive in phase so that constructive interference yields maximum amplitude ( A + A = 2A ).
Part (d): Displacement-Time Sketch for Point S
Sketch, on Figure 7, a graph to show how the displacement of S varies with t.
✅ Correct Answer Features
- Starts at a displacement of +4 mm when t = 0 (matching position of point S on Figure 6).
- Sinusoidal wave shape with an amplitude of 4 mm .
- Correct period: T = 1 / f = 1 / 625 = 1.6 ms (one full cycle completes at t = 1.6 ms on the grid axis).
🧠 Marking Breakdown (3 Marks)
- Mark 1: Sinusoidal curve starting at initial displacement = +4 mm.
- Mark 2: Correct amplitude corresponding to point S ( 4 mm , not 8 mm or 3.5 mm).
- Mark 3: Correct period mapped across the time axis ( 1.6 ms for one complete cycle).
❌ Common Errors
Students frequently confuse displacement-distance graphs with displacement-time graphs, mistakenly plotting spatial wavelengths instead of calculating the temporal time period T = 1 / f .
Topics
Physics · Practical skills · Required Practicals · 3.3 Waves · Data analysis · AS practicals (1–6)
Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.