AQA AS Level Physics Paper 2, June 2023: Question 17

1 mark · Medium difficulty · Multiple Choice

Calculate the path difference between two aerials receiving radio waves from a distant transmitter, given the wave frequency and phase difference.

Practise this question

Question

Multiple choice question 17 asking for the difference in distance A1T - A2T between two aerials receiving 88 MHz radio waves with a phase difference of 6.6 rad. Four options are given: A 1.6 m, B 3.2 m, C 3.6 m, and D 7.2 m.
Question text

17 Two aerials A1 and A2 receive radio waves from the same distant transmitter T.

The waves have a frequency of 88 MHz.

The phase difference between the waves received by A1 and A2 is 6.6 rad.

What is the distance A1T – A2T?

[1 mark]

A 1.6 m

B 3.2 m

C 3.6 m

D 7.2 m

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 17 is option C, corresponding to a distance of 3.6 m.

17 C 3.6 m

How to answer it

Radio Waves: Phase and Path Difference

AQA AS Level Physics • Waves • Multiple Choice

What this question tests

This question assesses your understanding of the relationship between path difference and phase difference for progressive waves. You need to confidently convert between radians and wavelengths, calculate wavelengths using wave speed and frequency, and interpret path difference notation like A₁T - A₂T .

Question 17

Relating Phase Difference to Path Difference

✅ Correct Answer

C (3.6 m)

Mark awarded: 1 / 1 for selecting option C.

💡 Key Knowledge

  • Phase vs Path: A full cycle corresponds to a phase difference of 2π rad and a path difference of one wavelength (λ).
  • Wave Equation: c = fλ , where c is the speed of electromagnetic waves in a vacuum/air ( 3.00 × 10⁸ m s⁻¹ ).
  • Formula: Path Difference = (φ / 2π) × λ

🧠 Exam Technique

  • For multiple-choice calculations, write down your intermediate steps on the question paper to avoid calculator punch errors.
  • Keep values in standard form or full calculator display until the final rounding step.

❌ Common Errors

  • Forgetting powers of ten: Failing to convert MHz to Hz ( 88 MHz = 88 × 10⁶ Hz ).
  • Radians confusion: Treating the 6.6 rad phase difference as degrees or dividing by 360 instead of 2π.

📐 Step-by-Step Calculation

  1. Find the wavelength (λ):
     Using λ = c / f
    λ = (3.00 × 10⁸ m s⁻¹) / (88 × 10⁶ Hz) = 3.409 m
  2. Relate phase difference to path difference:
     Path difference = (φ / 2π) × λ
    Path difference = (6.6 / (2 × π)) × 3.409 m
  3. Calculate final value:
     Path difference = 1.0504 rad-fraction × 3.409 m ≈ 3.58 m ≈ 3.6 m (matching option C).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.