AQA AS Level Physics Paper 2, November 2021: Question 15

1 mark · Medium difficulty · Multiple Choice

Determine the position of a point X on a rope carrying a progressive wave after a given time interval, given the wave's frequency, wavelength, and amplitude.

Practise this question

Question

A multiple-choice question showing a diagram of a progressive wave traveling along a rope from M to N with an arrow indicating the direction of energy transfer. Point X is marked on the rope where it crosses the equilibrium line. Below the diagram, text states the wave has a frequency of 5.0 Hz, wavelength 1.0 m, and amplitude 0.20 m, and asks where X will be after 0.15 s. Four options are given: A (below MN by 0.20 m), B (above MN by 0.20 m), C (nearer N by 0.15 m), and D (nearer N by 0.75 m), each with a selection box.
Question text

15 A progressive wave travels along a rope in the direction M to N.

X marks a point on the rope.

The wave has a frequency of 5.0 Hz, a wavelength of 1.0 m and an amplitude of 0.20 m.

Where will X be after 0.15 s?

[1 mark]

A below MN by 0.20 m

B above MN by 0.20 m

C nearer N by 0.15 m

D nearer N by 0.75 m

Mark scheme

Show the mark scheme The mark scheme table shows that question 15 corresponds to option B, which is 'above MN by 0.20 m'.

15 B above MN by 0.20 m

How to answer it

Progressive Waves: Motion of a Particle on a Rope

What this question tests

This question assesses your understanding of transverse progressive waves, specifically distinguishing between the motion of the wave profile (energy transfer) and the simple harmonic motion of individual particles on the medium. It tests your ability to calculate time periods, phase differences, and particle displacements over a given time interval.

Question 15 Analysis

Multiple Choice Question (1 Mark)

✅ Correct Answer

B: above MN by 0.20 m

Mark Scheme: Option B

💡 Key Knowledge

  • In a transverse progressive wave, particles oscillate perpendicular to the direction of energy transfer (up and down).
  • Particles do not travel along with the wave; they stay at their equilibrium horizontal position and vibrate vertically.
  • The maximum displacement of a particle from equilibrium is equal to the amplitude ( 0.20 m ).

🧠 Exam Technique

Do not confuse the motion of the wave profile (which moves towards N) with the motion of individual particles (which oscillate about the line MN). Rule out options C and D immediately because particles oscillate vertically, they do not travel horizontally along the rope!

❌ Common Errors

  • Choosing C or D because they mistook particle displacement for wave displacement along the rope.
  • Forgetting how to link time elapsed to the fraction of a wave cycle, leading to incorrect guesswork on particle position.

📐 Step-by-Step Calculation

  1. Find the time period ( T ) of the wave:
    Use T = 1 / f
    T = 1 / 5.0 Hz = 0.20 s
  2. Compare the elapsed time to the period:
    The question asks where point X is after t = 0.15 s .
    Calculate the fraction of a full cycle: t / T = 0.15 s / 0.20 s = 3 / 4 (or 0.75 of a cycle).
  3. Track the particle's motion:
    Point X starts on the equilibrium line ( MN ) heading upwards (since the wave travels left-to-right from M to N, points ahead on the wave profile dictate initial motion, or follow standard sine wave progression).
    After 3/4 of a full cycle ( 0.75 T ), a particle starting at equilibrium moves up to the positive crest, down through equilibrium, down to the negative trough, and 3/4 of the way brings it to the positive maximum displacement (crest).
    Therefore, its displacement is equal to the amplitude: +0.20 m (above MN ).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.