AQA AS Level Physics Paper 2, June 2025: Question 9

1 mark · Medium difficulty · Multiple Choice

Calculate the speed of a progressive wave given the frequency and the distance corresponding to a phase difference of pi/2.

Practise this question

Question

Question 9: The minimum distance between two points on a progressive wave with a phase difference of pi/2 is 0.040 m. The frequency of the wave is 400 Hz. What is the speed of the wave? Four options are given: A is 16 m s^-1, B is 32 m s^-1, C is 64 m s^-1, and D is 128 m s^-1.

Mark scheme

Show the mark scheme Mark scheme for question 9 showing the correct option is C, corresponding to 64 m s^-1, categorized under assessment objective AO1.

How to answer it

Wave Speed from Phase Difference & Frequency

📌 What this question tests

This multiple-choice question assesses your ability to relate phase difference (in radians) to spatial separation (distance along a wave), determine the full wavelength (λ), and apply the wave speed equation (c = fλ) to calculate wave speed.

Question 09 • Multiple Choice [1 Mark]

Determining Progressive Wave Speed

AQA AS Level Physics — Waves

✅ Correct Answer

C: 64 m s⁻¹

Mark Scheme Breakdown:
• 1 mark (AO1): Correct option selected (C).

💡 Key Knowledge

  • A full wave cycle corresponds to a phase change of 2π rad (or 360°), which spans one full wavelength λ .
  • Phase difference equation:
    Δφ = (2π × Δx) / λ
  • Since π/2 rad is one-quarter of a full cycle ( 2π / 4 ), the distance between these two points corresponds to one-quarter of a wavelength: Δx = λ / 4 .
  • Wave speed equation:
    c = fλ (or v = fλ )

📐 Step-by-Step Calculation

  1. Find the fraction of a full cycle:
    Phase difference = π/2 rad
    Fraction of cycle = (π / 2) / 2π = 1/4
  2. Calculate wavelength (λ):
    Distance Δx = λ / 4 = 0.040 m
    λ = 4 × 0.040 m = 0.16 m
  3. Calculate wave speed (c):
    Frequency f = 400 Hz
    c = f × λ = 400 Hz × 0.16 m = 64 m s⁻¹

🧠 Exam Technique & Quick Check

  • Proportional reasoning saves time: Instead of rearranging the full radian formula under timed pressure, spot right away that π/2 is a quarter-turn, so the full wave is simply 4 times longer: 4 × 0.040 = 0.16 m .
  • Sanity-check the multiples: Notice the options are Powers of 2 multiples: 16, 32, 64, 128. Each corresponds to a factor-of-two mistake in handling π/2 .

❌ Common Errors & Distractor Traps

  • Trap A (16 m s⁻¹): Treating 0.040 m directly as the full wavelength λ ( c = 400 × 0.040 = 16 ).
  • Trap B (32 m s⁻¹): Confusing π/2 rad with half a wave ( π rad ) and only doubling: λ = 0.080 m , giving 400 × 0.080 = 32 .
  • Trap D (128 m s⁻¹): Multiplying by 8 instead of 4 (e.g., misinterpreting π/2 as 1/8 of a cycle by incorrectly using 4π ).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.