Given that v, f and $\lambda$ are the velocity, frequency and wavelength of a wave respectively. Which of the following equations is correct?

Analyze the question: You need the correct relationship between wave velocity (v), frequency (f) and wavelength (λ).

Concept: The wave equation says that a wave travels a distance of one wavelength (λ) in one period (T). So:

v = distance / time = λ / T

Since frequency f = 1/T, this becomes:

v = fλ

Step-by-step solution:

1. Start with the wave equation: v = fλ
2. Make f the subject by dividing both sides by λ: f = v/λ

Checking each option:

• A. v = f²λ: Wrong. The frequency is not squared. The correct form is v = fλ.
• B. f = v/λ: Correct. It is a direct rearrangement of v = fλ.
• C. f = v/λ²: Wrong. The wavelength should not be squared.
• D. λ = f/v²: Wrong. The correct form is λ = v/f.

Unit check: v/λ has units (m/s) ÷ m = 1/s = Hz, which is the unit of frequency. Option B passes. The other options do not give consistent units.

Answer: B.

Exam tip: Remember the "VFL" triangle, with v on top and f and λ at the bottom. Cover the quantity you want and read off the formula:

• Cover v → v = f × λ
• Cover f → f = v/λ
• Cover λ → λ = v/f

Also, any option with a squared term in a basic wave equation is almost always a trap.