AQA AS Level Physics Paper 2, June 2022: Question 17

1 mark · Medium difficulty · Multiple Choice

Calculate the new frequency of the first harmonic of a stretched wire when its tension is doubled.

Practise this question

Question

Multiple choice question 17 asking for the new frequency of the first harmonic of a vibrating wire when its tension is doubled from an initial frequency of 300 Hz. Four options are given: A 150 Hz, B 420 Hz, C 600 Hz, and D 1200 Hz.
Question text

17 A stretched wire vibrates between two fixed points.

The frequency of the first harmonic of the vibrating wire is 300 Hz.

Without making any other change, the tension in the wire is doubled.

What is the frequency of the new first harmonic of the wire?

[1 mark]

A 150 Hz

B 420 Hz

C 600 Hz

D 1200 Hz

Mark scheme

Show the mark scheme Mark scheme for question 17 indicating the correct answer is option B (420 Hz).

17 B (AO1) 420 Hz

How to answer it

Vibrating Wire Frequency and Tension

What this question tests

This question assesses your understanding of stationary waves on stretched strings, specifically how the frequency of the first harmonic depends on the tension within the wire. It tests proportional reasoning and the application of the relevant algebraic relationship without requiring full numerical calculation from scratch.

Question 17 [1 mark]

Exam Breakdown

✅ Correct Answer

B (420 Hz)

Mark: 1 / 1 (AO1 - Demonstration of Knowledge)

💡 Key Knowledge

  • The formula for the frequency of the first harmonic on a stretched string is f = (1 / 2L) × √(T / μ) .
  • Since length ( L ) and mass per unit length ( μ ) remain constant, frequency is directly proportional to the square root of the tension ( f ∝ √T ).

🧠 Exam Technique

When a multiple-choice question asks about scaling effects (e.g., "tension is doubled"), set up a ratio or proportionality statement rather than punching long decimals into your calculator early. Keep intermediate values exact.

❌ Common Errors

Many students incorrectly assume a linear relationship ( f ∝ T ) and double the frequency directly to get 600 Hz (Option C). Always check whether variables inside square roots or powers are involved!

📐 Step-by-Step Calculation

  1. Identify the proportionality: Frequency f is proportional to √T because length and mass per unit length are unchanged.
  2. Set up the scaling factor: If tension T is doubled (multiplied by 2 ), the new frequency is multiplied by √2 .
  3. Perform the arithmetic:
    New frequency = 300 Hz × √2
    New frequency = 300 × 1.4142... = 424.26 Hz
  4. Match with options: Rounding or comparing standard values leads directly to option B (420 Hz).

Topics

Physics · Required Practicals · 3.3 Waves · AS practicals (1–6)

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.