IGCSE 0625 / Section 3.1 / Core

Speed, frequency, wavelength.

Every wave obeys one tidy rule that ties together how fast it moves, how often it wiggles, and how long each wiggle is. Pin down any two and the third follows at once.

The key idea

The wave speed equals the frequency multiplied by the wavelength: v = f times wavelength. At a fixed speed, raising the frequency shortens the wavelength, and lowering it lengthens the wavelength.

Definition · learn the exact words

The wave equation states that the wave speed equals the frequency multiplied by the wavelength.

v = f λ  (speed in m/s, frequency in Hz, wavelength in m)

Rearranged: f = v ÷ λ and λ = v ÷ f.

Section 01

Tie the three together.

Adjust the frequency and wavelength and watch the wave speed that results.

Stage 1 · Learn

Check wave equation

Four quick checks. Each correct answer earns XP and lights this skill on your star map.

Quick check+10 XP

The wave equation is...

Quick check+10 XP

In the wave equation, wave speed equals...

Quick check+10 XP

At a constant wave speed, if the frequency increases the wavelength...

Quick check+10 XP

To find the wavelength from speed and frequency you use...

Section 02

One equation, three rearrangements.

Knowing any two of speed, frequency and wavelength gives you the third.

v = f λ  (speed = frequency × wavelength)
f = v ÷ λ  and  λ = v ÷ f
Worked example

A wave has a frequency of 50 Hz and a wavelength of 2.0 m. Find its speed.

Step 1 · Write the equationv = f λ
Step 2 · Substitutev = 50 × 2.0
Step 3 · Answerv = 100 m/s
Examiner trap

Keep the units consistent and rearrange with care. To find wavelength, divide speed by frequency; to find frequency, divide speed by wavelength. Mixing these up is the most common slip.

Stage 2 · Exam

Exam-style questions

Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 2.

Finish the four checks above to unlock the exam questions
Exam style+20 XP

A wave has a frequency of 50 Hz and a wavelength of 2.0 m. Its speed is...

Exam style+20 XP

A sound wave travels at 340 m/s with a frequency of 170 Hz. Its wavelength is...

Exam style+20 XP

Water waves of wavelength 0.50 m pass a post at 4.0 waves per second. Their speed is...

Skill unlocked

Wave equation, mastered.

Two wave skills down. Keep the chain going.

-Rank -Level -Score -Topics
Go deeper · practice
Six original Cambridge-style questions
The v = f times wavelength relationship and its rearrangements for frequency and wavelength. Attempt each, then reveal the worked solution.
Stage 3 · master the unit
Waves challenge
Mixed questions across the whole unit, each one worth XP. Start this only when you feel confident across every topic in the unit, not just wave equation.
Start the unit challenge →