AQA A-Level Physics Paper 1, June 2025: Question 2
10 marks · Medium difficulty · Extended Answer
Explain transverse and stationary wave properties on a wire, and calculate wire properties to determine which wire and tension allows the first five harmonics to be produced within a given frequency range.
Practise this questionQuestion
Question text
02.1 State what is meant by a transverse wave.
[2 marks]
Figure 2 shows apparatus that is used to investigate stationary waves on a
stretched wire.
Figure 2
A block of weight W is used to keep the wire under tension.
The frequency of the ac supply is varied until a stationary wave is produced on
the wire.
02.2 Explain how a stationary wave is produced on the wire.
[1 mark]
02.3 Figure 3 shows a small section of the wire at one instant.
Five points on the wire are labelled P1 to P5.
The dashed line represents the position of the wire when the ac supply is turned off.
Figure 3
Describe how the phase of the oscillating particles varies along the wire
between P1 and P5.
[2 marks]
02.4 A student investigates stationary waves on a wire using the apparatus in Figure 2.
The investigation requires the student to produce the first five harmonics on the wire.
The student needs to choose one of two wires, A or B, for the investigation.
The mass of a 2.00 m length of wire A is 1.32 g.
The mass of a 2.00 m length of wire B is 2.94 g.
The ac supply can produce signals in the range 1 Hz to 50 Hz.
The length of the wire that vibrates between the vibration generator and the pulley
is 1.50 m.
The student needs to choose one value for weight W for the investigation.
W can be either 1.0 N or 5.0 N.
Determine, in kg m−1, the mass per unit length of each wire.
Go on to suggest which wire and which value of W the student should use to produce
*05*the first five harmonics.
[5 marks]
mass per unit length of A = kg m–1
mass per unit length of B = kg m–1
wire = W = N
Mark scheme
Show the mark scheme
02.1 Idea that the oscillations (of particles in the wave) are at Allow ‘oscillates’ for ‘oscillations’. Do not 2 AO1
right angles 1 accept ‘vibrations’.
Allow ‘displacement’ for ‘oscillations’
Credit a correctly labelled diagram
Do not allow a contradiction in 1
to the direction of energy transfer 2
2 is contingent on 1 .
Do not allow direction of (wave) motion/travel
Treat any reference to polarisation as neutral.
If no other mark given: award max 1 when
answer suggests that amplitude is
perpendicular to the direction of energy
transfer.
Question Answers Additional comments/Guidance Mark AO
02.2 Idea that waves (from vibration generator and reflected If a reflected wave is referred to, the 1 AO1
wave) travel in opposite directions (along the wire) and presence of an incident wave can be
superpose assumed.
Do not accept ‘interfere’ for ‘superpose’
Do not accept reference to ‘phase
(difference)’unless correct, ie a valid
comment would be ‘phase difference is time
dependent’.
02.3 Idea that particles in wave between P1 and P3 are in phase 2 AO2
OR If no other mark given: award max 1 for ‘P1
and P3 and P5 are nodes’ and ‘P2 and P4
between P3 and P5 are in phase 1
are antinodes’ provided that there is no
reference to a phase relationship between the
nodes.
Reject: ’completely out of phase’ or ‘out of
Idea that particles between P1 and P3 are in antiphase with
phase’ for antiphase; allow ‘π out of phase’ or
particles between P3 and P5
‘180 degrees out of phase’.
OR
idea that P2 and P4 are in antiphase 2
02.4 Determines mass per unit length for either wire and answer A μ = 6.60 × 10−4 kg m−1 5 1 × AO1
seen on answer line 1 −3 −1
B μ = 1.47 × 10 kg m 4 × AO3
Allow incorrect values of mass per unit length
to be carried forward from 1 to the rest of
the answer except 5 .
Expect to see values from:
Determines frequency of first harmonic f1 for one wire and
value of W 2 W / A A B B
N f1 / Hz 5f1/Hz f1 / Hz 5f1 / Hz
Evidence of use of 5f1 to determine the frequency range 1.0 13.0 65.0 8.7 43.5
OR
evidence of required frequency ≤10 Hz 3 5.0 29.0 145 19.4 97.0
Comparison between the fifth-harmonic (frequency) For 4 , look for some idea that their selected
and 50 Hz. 4 fifth-harmonic frequency is the greatest that
does not exceed 50 Hz or that first-harmonic
is greatest that does not exceed 10 Hz.
Allow reference to ‘range’ for values of
frequency.
4 does not require a value for the fifth
harmonic.
Wire B and W = 1.0 N 5 B can be identified by its mass or mass per
unit length.
MP5 is a standalone mark and can be
awarded without further evidence.
Alternative 2 , 3 and 4 For alternative 2 expect to see one from:
W / A B
2 Calculates a wavelength (or half wavelength) for 50 Hz
N wavelength wavelength
and any one combination of wire and weight. / m / m
3 Evidence of maximum wavelength (or half wavelength) 1.0 0.78 0.52
of fifth harmonic is 1.5/(5/2) or 0.6m (or 1.5/2 or 0.3 m).
5.0 1.74 1.17
4 compares between their combination wavelength and
their fifth harmonic maximum wavelength.
If alternative methods are used: 2 is for
using the frequency formula, 3 is for a
calculation that allows the comparison; 4 is
for the comparison.
Total 10
How to answer it
Investigating Stationary Waves on a Stretched Wire
What this question tests
- Wave fundamentals: Accurate definition of a transverse wave using precise scientific terminology.
- Wave interference: Describing the formation of stationary waves via superposition of counter-propagating waves.
- Phase relationships: Differentiating between nodes, antinodes, and identifying phase/antiphase particle motion in stationary waves.
- Experimental design & harmonics: Applying the fundamental frequency formula f = (1 / 2L) × √(T / μ) , calculating mass per unit length, and constraining variables to fit within an apparatus frequency limit (1 Hz – 50 Hz).
Definition of a Transverse Wave
2 Marks • Assessment Objective: AO1
✅ Model Answer
Oscillations (or displacements) of particles are perpendicular / at right angles [1 mark]
to the direction of energy transfer [1 mark].
💡 Key Knowledge
- Waves transfer energy without transferring matter.
- In transverse waves (e.g., waves on a string, EM waves), particle oscillations are at 90° to energy propagation.
- In longitudinal waves (e.g., sound), oscillations are parallel to energy propagation.
🧠 Exam Technique
Always state "direction of energy transfer" instead of simply "direction of the wave". Examiners penalise ambiguous phrasing such as "direction of wave motion" or "wave travel".
❌ Common Errors
- Writing vibrations instead of oscillations or displacement.
- Stating "amplitude is perpendicular" (amplitude is a scalar maximum value, not the motion itself).
- Saying "perpendicular to the wave" without mentioning energy transfer.
Formation of a Stationary Wave
1 Mark • Assessment Objective: AO1
✅ Model Answer
Two waves of the same frequency/wavelength travelling in opposite directions (the incident wave from the generator and the reflected wave from the fixed end/pulley) superpose (or combine/add together).
❌ Common Errors
- Using the word interfere instead of superpose. The mark scheme explicitly notes: Do not accept 'interfere' for 'superpose'.
- Forgetting to state that the reflected wave travels in the opposite direction to the incident wave.
Phase Variation Between Points P₁ and P₅
2 Marks • Assessment Objective: AO2
✅ Model Answer
- Particles in the same loop (e.g., between P₁ and P₃, OR between P₃ and P₅) are in phase [1 mark].
- Particles in adjacent loops (between P₁ and P₃ compared to between P₃ and P₅, or points P₂ and P₄) are in antiphase (or π radians / 180° out of phase) [1 mark].
💡 Key Knowledge: Stationary Wave Phase Rules
- Within one loop (between two adjacent nodes): All vibrating particles are completely in phase (they reach maximum displacement at the same instant), although their amplitudes differ.
- In adjacent loops: Particles are in antiphase (moving in opposite directions at any given moment).
- Nodes (P₁, P₃, P₅): Zero amplitude at all times.
❌ Common Errors
- Vague phrasing like "completely out of phase" or "out of phase" without specifying antiphase, 180°, or π radians.
- Treating it like a progressive wave and assuming phase varies continuously with distance Δφ = (2π / λ) × Δx .
Experimental Choice: Wire and Weight Selection
5 Marks • Assessment Objectives: 1 × AO1, 4 × AO3
📐 Step-by-Step Calculations
Step 1: Calculate mass per unit length (μ) for both wires
Convert masses to kg:
Mass of wire A = 1.32 g = 1.32 × 10⁻³ kg
Mass of wire B = 2.94 g = 2.94 × 10⁻³ kg
μ = mass / length = m / 2.00 m
- Wire A: μA = (1.32 × 10⁻³ kg) / 2.00 m = 6.60 × 10⁻⁴ kg m⁻¹
- Wire B: μB = (2.94 × 10⁻³ kg) / 2.00 m = 1.47 × 10⁻³ kg m⁻¹
Step 2: Apply the fundamental frequency equation
The length of vibrating wire is L = 1.50 m , so 2L = 3.00 m .
f₁ = (1 / 2L) × √(T / μ) = (1 / 3.00) × √(W / μ)
To produce the first five harmonics, the 5th harmonic ( f₅ = 5f₁ ) must NOT exceed the signal generator's maximum frequency of 50 Hz:
5f₁ ≤ 50 Hz ⇒ f₁ ≤ 10 Hz
Step 3: Test the combinations of wire and weight
| Wire | Weight W | First Harmonic f₁ (Hz) | 5th Harmonic 5f₁ (Hz) | Fits within 50 Hz limit? |
|---|---|---|---|---|
| A (6.60 × 10⁻⁴ kg m⁻¹) | 1.0 N | 13.0 Hz | 65.0 Hz | ❌ Too high (> 50 Hz) |
| A (6.60 × 10⁻⁴ kg m⁻¹) | 5.0 N | 29.0 Hz | 145 Hz | ❌ Too high (> 50 Hz) |
| B (1.47 × 10⁻³ kg m⁻¹) | 5.0 N | 19.4 Hz | 97.0 Hz | ❌ Too high (> 50 Hz) |
| B (1.47 × 10⁻³ kg m⁻¹) | 1.0 N | 8.7 Hz | 43.5 Hz | ✅ Fits (≤ 50 Hz) |
✅ Final Answers & Mark Breakdown
- mass per unit length of A: 6.60 × 10⁻⁴ kg m⁻¹
- mass per unit length of B: 1.47 × 10⁻³ kg m⁻¹ [1 mark]
- Calculates f₁ for at least one wire/weight combination [1 mark].
- Shows condition 5f₁ or f₁ ≤ 10 Hz [1 mark].
- Compares 5th harmonic to 50 Hz [1 mark].
- Selects Wire B and W = 1.0 N [1 mark standalone].
❌ Common Calculation Traps
- Length Confusion: Dividing mass by 1.50 m instead of 2.00 m when calculating μ. The sample weighed was 2.00 m!
- Unit Conversion: Forgetting to convert grams to kilograms ( × 10⁻³ ), giving values of μ off by a factor of 1000.
- Overlooking the 5th Harmonic: Only checking if f₁ ≤ 50 Hz rather than 5f₁ ≤ 50 Hz . All combinations have f₁ < 50 Hz , but only one allows the 5th harmonic to be reached!
Topics
Physics · Practical skills · Required Practicals · 3.3 Waves · AS practicals (1–6) · Data analysis
Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.