AQA AS Level Physics Paper 2, June 2024: Question 15

1 mark · Medium difficulty · Multiple Choice

Determine the distance between two coherent microwave sources required to produce the next maximum of intensity at a given point.

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Question

Multiple choice question 15 featuring a diagram showing two coherent microwave sources M1 and M2 located 1.0 m away from a point D. Source M2 is moved away along a perpendicular line, and four options for the distance to the next maximum are given as A (5.0 cm), B (10 cm), C (16 cm), and D (32 cm).
Question text

15 Sources M1 and M2 emit coherent microwaves of wavelength 5.0 cm.

When M1 and M2 are very close, a maximum of intensity occurs at a point D that is 1.0 m

away.

M2 is moved away from M1 along the line perpendicular to M1D.

The next maximum of intensity occurs at D when the distance between M1 and M2 is

[1 mark]

A 5.0 cm

B 10 cm

C 16 cm

D 32 cm

Mark scheme

Show the mark scheme Mark scheme for question 15 indicating the correct answer is D, corresponding to 32 cm.

15 D 32 cm

How to answer it

Microwave Interference & Path Difference

AQA AS Level Physics • Waves • Multiple Choice Question

What this question tests

This question assesses your deep understanding of wave superposition, coherence, path difference, and constructive interference. Specifically, it tests whether you can apply Pythagoras' theorem to calculate path lengths when two sources are separated perpendicularly, moving beyond standard double-slit approximation formulas.

Question 15 Analysis

Interference of Coherent Microwaves

✅ Correct Answer

D (32 cm)

Mark Awarded: 1 / 1

💡 Key Knowledge

  • Constructive Interference: Occurs when path difference = nλ (where n = 0, 1, 2...).
  • Coherence: Sources M₁ and M₂ maintain a constant phase relationship and the same frequency/wavelength (λ = 5.0 cm).
  • Initial State: When very close together, path difference is effectively zero (n = 0 maximum at D).

🧠 Exam Technique

  • Do not blindly apply the standard fringe spacing formula ( ω = λD / s ), because the separation s is not much smaller than the distance D as M₂ moves further away.
  • Set up exact path lengths using right-angled triangles and Pythagoras' theorem.

❌ Common Errors

Many students incorrectly choose option A (5.0 cm) by assuming the next maximum simply increases by one wavelength of separation, or they incorrectly use small-angle approximations which break down here.

📐 Step-by-Step Calculation

  1. Identify initial conditions: Both sources are at distance D = 1.0 m (100 cm). Path difference = 0 cm (zeroth-order maximum).
  2. Set condition for the next maximum: For the next intensity maximum (n = 1), the path difference between the two waves arriving at D must increase by exactly one wavelength:
    Path Difference = 1 × λ = 5.0 cm = 0.05 m
  3. Formulate the path lengths: Let the separation between M₁ and M₂ be x .
    • Distance from M₁ to D = 1.0 m
    • Distance from M₂ to D = √(1.0² + x²)
  4. Equate path difference:
    √(1.0² + x²) - 1.0 = 0.05
    √(1.0 + x²) = 1.05
  5. Solve for separation x :
    1.0 + x² = (1.05)²
    1.0 + x² = 1.1025
    x² = 0.1025
    x = √0.1025 ≈ 0.320 m = 32 cm

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.