AQA AS Level Physics Paper 2, June 2022: Question 15

1 mark · Medium difficulty · Multiple Choice

Determine the wavelength of a progressive wave given the distance and phase difference between two points P and Q.

Practise this question

Question

Multiple choice question 15 featuring a graph of a progressive wave with displacement y against position x. Two points P and Q are labeled on the wave separated by a horizontal distance d. Four options A, B, C, and D are given as algebraic expressions involving d, theta, and pi.
Question text

15 Two points P and Q on a progressive wave are separated by distance d.

The phase difference between P and Q is θ rad.

What is the wavelength?

[1 mark]

d

A

2π

B θd

2πd

C

d

D

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is C, with the corresponding algebraic expression 2 pi d / theta.

2 d

15 C (AO2)

How to answer it

Wavelength and Phase Difference

AQA AS Level Physics • Waves

What this question tests

This question assesses your understanding of progressive waves, specifically the mathematical relationship linking phase difference, separation distance between two points, and wavelength. It tests AO2 (Application) by requiring you to rearrange a standard wave equation for an unknown variable based on graphical information.

Question 15 Multiple-Choice Breakdown

Two points P and Q on a progressive wave are separated by distance d. The phase difference between them is θ rad. What is the wavelength?

Marks available: 1 mark | Correct Option: C

✅ Correct Answer: C

The correct expression for the wavelength is 2πd / θ .

💡 Key Knowledge

  • The phase difference formula relates phase (θ), distance separation (d), and wavelength (λ): θ = (2π / λ) × d
  • A full cycle corresponds to a distance of one wavelength ( λ ) and a phase angle of 2π radians.

🧠 Exam Technique

  • Don't get distracted by the visual placement of points P and Q on the displacement-distance graph—the question already provides algebraic symbols for distance ( d ) and phase ( θ ).
  • Always start by writing down the standard equation you know, then carefully rearrange it step-by-step for the target variable.

❌ Common Errors

  • Inverting the fraction and choosing Option A ( θd / 2π ), which is the formula rearranged for phase difference or wavelength incorrectly inverted.
  • Forgetting the factor of 2π and assuming phase scales linearly as just distance divided by wavelength.

📐 Step-by-Step Derivation

  1. Step 1: State the standard formula linking phase difference, distance, and wavelength:
    θ = (2π / λ) × d
  2. Step 2: Rearrange to make wavelength ( λ ) the subject. Multiply both sides by λ :
    θ × λ = 2πd
  3. Step 3: Divide both sides by θ :
    λ = 2πd / θ
  4. Step 4: Match your final derived expression to the multiple-choice options to select C.

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.