AQA AS Level Physics Paper 2, November 2021: Question 17

1 mark · Medium difficulty · Multiple Choice

Determine the next harmonic at which points P and Q on a stretched string will oscillate in phase, given their positions and initial vibration at the first harmonic.

Practise this question

Question

A diagram shows a string stretched between two fixed points O and R, which are 120 cm apart, with points P at 30 cm and Q at 90 cm from O marked with crosses. Below the diagram, text asks for the next harmonic at which P and Q oscillate in phase when the frequency is increased from the first harmonic. Four multiple choice options are listed: A second, B third, C fourth, and D fifth, each with an oval selection box.
Question text

17 The diagram shows a string stretched between two fixed points O and R which are

120 cm apart.

P and Q are points on the string.

OP = 30 cm

OQ = 90 cm

At a certain frequency the string vibrates at its first harmonic.

P and Q oscillate in phase.

The frequency is gradually increased.

What is the next harmonic at which P and Q will oscillate in phase?

[1 mark]

A second

B third

C fourth

D fifth

Mark scheme

Show the mark scheme The mark scheme table shows the correct answer for question 17 is B, corresponding to the third harmonic.

17 B third

How to answer it

Stationary Waves on a Stretched String

Question 17 • Multiple Choice • 1 Mark

What this question tests

This question assesses your understanding of stationary waves on strings fixed at both ends, specifically the concept of harmonics, node and antinode positions, and phase relationships between different points along the string as frequency changes.

Question 17 Breakdown

Identifying Harmonics and Phase Relationships

✅ Correct Answer

B (third)

Mark Awarded: 1 / 1 for selecting option B.

💡 Key Knowledge

  • Total length of string, L = 120 cm .
  • Points P and Q are at 30 cm and 90 cm from end O respectively.
  • Points are in phase when they are separated by an integer multiple of a full wavelength or lie within the same loop (or loops moving in the exact same direction).

🧠 Exam Technique

Sketch out the harmonic profiles rapidly on your question paper. Visualising the displacement nodes and antinodes for higher harmonics makes phase comparison instant without relying purely on memorisation.

❌ Common Errors

Assuming adjacent loops always oscillate in phase. Remember that neighboring loops in a stationary wave are in anti-phase (180 degrees out of phase) because one goes up while the other goes down.

📐 Step-by-Step Analysis

  1. First Harmonic (Fundamental): The string forms a single loop of length L = 120 cm . The wavelength is 2L = 240 cm . P (at 30 cm) and Q (at 90 cm) are both within this single loop, meaning they always move up and down together (in phase).
  2. Second Harmonic: The string splits into 2 loops, each of length 60 cm . Node occurs at the center ( 60 cm ). P is at 30 cm (center of first loop) and Q is at 90 cm (center of second loop). These two loops oscillate in opposite directions (anti-phase), so P and Q are 180 degrees out of phase.
  3. Third Harmonic: The string splits into 3 equal loops, each of length 120 / 3 = 40 cm .
    • Loop 1: 0 cm to 40 cm (P at 30 cm is inside this loop)
    • Loop 2: 40 cm to 80 cm
    • Loop 3: 80 cm to 120 cm (Q at 90 cm is inside this loop)
  4. Since Loop 1 and Loop 3 are separated by one full loop (an intermediate loop), their displacements are in the exact same direction at any given time. Therefore, P and Q oscillate in phase again at the third harmonic.

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.