AQA A-Level Physics Paper 1, November 2020: Question 7

1 mark · Medium difficulty · Multiple Choice

Determine the SI unit for the constant k in the equation relating water wave speed and wavelength

Practise this question

Question

A multiple-choice question numbered 0 7 about water waves. The equation is given as v = sqrt(k * lambda), where v is wave speed, lambda is wavelength, and k is a constant. Four options for the SI unit of k are listed: A is m s^-2, B is m s^-1, C is m^(3/2) s^-1, and D is m^(1/2) s^-1.
Question text

07 Water waves of wavelength λ and wave speed v are related by v = k where k is a

constant.

What is a possible SI unit for k?

[1 mark]

A m s−2

B m s−1

m2 s−1

C

m2 s−1

D

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 07 is option A.

07 A

How to answer it

Determining SI Units from Wave Equations

📌 What this question tests

This question assesses your understanding of homogeneity of physical equations and your ability to manipulate and derive SI base units for constants within a given algebraic relationship. Specifically, it tests handling square roots in dimensional analysis.

Question 07

Finding the SI unit for constant k in v = √(kλ)

✅ Correct Answer

Option A: m s⁻²

Mark: 1 / 1

💡 Key Knowledge

  • Speed v has the SI unit m s⁻¹ .
  • Wavelength λ is a length, with the SI unit m .
  • Square roots can be written as fractional powers: √(kλ) = (kλ)^(1/2) .

🧠 Exam Technique

Rearrange the formula to make the unknown constant k the subject before substituting units. This prevents algebraic errors with square roots and powers.

❌ Common Errors

Students often forget to square both sides to eliminate the square root, leading them to mistakenly choose options featuring fractional powers like m^(3/2) s⁻¹ .

📐 Step-by-Step Derivation

  1. Start with the given equation:
    v = √(kλ)
  2. Square both sides to remove the square root sign:
    v² = kλ
  3. Rearrange to solve for k:
    k = v² / λ
  4. Substitute the SI units for velocity ( m s⁻¹ ) and wavelength ( m ):
    k = (m s⁻¹)² / m
  5. Expand the bracket:
    k = (m² s⁻²) / m
  6. Simplify the expression:
    k = m s⁻² (matching Option A)

Topics

Physics · 3.1 Measurements and their errors · 3.3 Waves

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.