AQA A-Level Physics Paper 1, June 2022: Question 18

1 mark · Medium difficulty · Multiple Choice

Identify the correct statement describing the motion of a particle in a longitudinal wave given its frequency and wave speed.

Practise this question

Question

Multiple-choice question 18. A longitudinal wave has a frequency of 660 Hz and a wave speed of 330 m/s. Four options are given: A, it travels at a speed of 330 m/s; B, it moves in phase with a particle 25 cm away; C, it oscillates with a time period of 1.5 ms; D, it changes direction 660 times every second.
Question text

18 A longitudinal wave of frequency 660 Hz travels through a medium.

The wave speed is 330 m s−1.

Which statement describes the motion of a particle in the wave?

[1 mark]

A It is travelling at a speed of 330 m s−1.

B It moves in phase with a particle in the wave 25 cm away.

C It oscillates with a time period of 1.5 ms.

D It changes direction 660 times every second.

Mark scheme

Show the mark scheme Mark scheme for question 18 showing the correct answer is C, with the explanation that the particle oscillates with a time period of 1.5 ms.

18 C (AO2) It oscillates with a time period of 1.5 ms.

How to answer it

Longitudinal Wave Particle Motion

📌 What this question tests

This question assesses your understanding of the fundamental kinematics of progressive waves (both transverse and longitudinal), specifically the relationship between wave frequency, wave speed, wavelength, and time period, as well as distinguishing between wave propagation speed and particle oscillation speed.

Question 18 [1 Mark]

Evaluating particle motion in a longitudinal wave

✅ Correct Answer: C

It oscillates with a time period of 1.5 ms.

The time period T is the reciprocal of frequency ( T = 1 / f ). Calculating 1 / 660 Hz gives approximately 0.00151 s , which is 1.5 ms .

💡 Key Knowledge

  • Wave Speed vs Particle Speed: Waves transfer energy through a medium, but individual particles oscillate back and forth about an equilibrium position—they do not travel along with the wave at the wave speed.
  • Time Period Formula: T = 1 / f
  • Wavelength Calculation: λ = c / f = 330 / 660 = 0.5 m (or 50 cm).

🧠 Exam Technique

Read through each option systematically and eliminate false statements using core definitions:

  • Check particle vs wave velocity.
  • Calculate wavelength to test phase relationships (particles are in phase separated by whole numbers of wavelengths, λ = 0.5 m or 50 cm , not 25 cm).
  • Quickly compute T = 1 / f to verify numerical options.

❌ Common Errors

  • Confusing A with particle motion: Believing that particles travel through the medium at the wave speed ( 330 m s⁻¹ ).
  • Phase misconceptions (Option B): Failing to calculate wavelength ( 50 cm ) and incorrectly assuming a separation of 25 cm ( λ / 2 ) puts particles in anti-phase, not in phase.
  • Frequency misinterpretation (Option D): Thinking frequency represents directional changes rather than complete oscillation cycles (though a particle changes direction twice per cycle, the frequency itself is 660 Hz , meaning 660 complete cycles per second, resulting in 1320 directional changes per second).

📐 Step-by-Step Calculation Breakdown

  1. Identify given variables: Frequency f = 660 Hz , Wave speed c = 330 m s⁻¹ .
  2. Calculate time period: Use T = 1 / f → T = 1 / 660 = 0.001515 s .
  3. Convert units to milliseconds: Multiply by 1000 → 1.515 ms ≈ 1.5 ms . Matches option C!
Mark Scheme Allocation: 1 mark awarded for selecting C. (AO2 - Application of knowledge to calculate and interpret wave parameters).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.