The wave speed equation

The wave speed equation is v = fλ: wave speed = frequency × wavelength. Speed is in metres per second (m/s), frequency in hertz (Hz) and wavelength in metres (m). It works for every kind of wave: sound, water waves, waves on a string and light. The related frequency equation, f = 1/T, links frequency to the period T, the time for one complete wave.

The wave speed formula

λ is the Greek letter lambda. One hertz means one wave per second, so 1 Hz is the same as 1 s⁻¹.

Why v = fλ

If 5 waves pass a point every second and each is 2 m long, then 5 × 2 = 10 m of wave passes each second. So the wave is moving at 10 m/s. Multiplying how many waves per second by the length of each gives the distance per second, which is the speed.

Rearranging the wave equation

The Wave Speed Calculator rearranges it for you and handles the unit prefixes.

Wavelength on a graph

The graph shows a wave frozen at one instant. Here x is the distance along the wave in metres and y is how far each point is displaced from its rest position.

The wavelength is the distance from one crest to the next, here 2 m. You can measure it between any two matching points, such as trough to trough. The amplitude is the maximum displacement from the rest position, here 0.5 m. Amplitude does not appear in v = fλ: a bigger wave carries more energy, but it does not travel faster.

The frequency equation: f = 1/T

The period T is the time for one complete wave to pass a point, in seconds. Frequency and period are reciprocals of each other:

A wave with a period of 0.02 s has a frequency of 1 ÷ 0.02 = 50 Hz, the frequency of the UK mains electricity supply. Combining the two equations gives another form of the wave speed equation, v = λ ÷ T: one wavelength travelled in one period.

Wave speed equation: worked examples

Example 1: sound

A note of frequency 440 Hz has a wavelength of 0.78 m in air. Find the speed of sound.

Example 2: water waves

Water waves travel across a pond at 0.6 m/s with a frequency of 2 Hz. Find their wavelength.

Example 3: radio waves

A radio station broadcasts at 100 MHz. Radio waves travel at the speed of light, 3.0 × 10⁸ m/s. Find the wavelength.

Convert first: 100 MHz = 100 × 10⁶ Hz = 1.0 × 10⁸ Hz.

Example 4: using distance and time first

A wave travels 12 m in 4 s and its wavelength is 0.5 m. Find its frequency.

First the speed: v = distance ÷ time = 12 ÷ 4 = 3 m/s. Then f = v ÷ λ = 3 ÷ 0.5 = 6 Hz.

Example 5: light in glass

Light of frequency 5.0 × 10¹⁴ Hz travels through glass at 2.0 × 10⁸ m/s. Find its wavelength in the glass.

That is 400 nm. When light enters glass, its frequency stays the same but it slows down, so its wavelength gets shorter. That change of speed is what causes refraction.

Now try one. Use the wave equation, then press Mark to check your answer in the course.

Speeds of common waves

The speed of a wave depends on the material it travels through, not on its frequency. Change the frequency of a sound in air, and the wavelength changes to keep v the same.

Measuring wave speed in a ripple tank

Measuring the speed of water waves is one of the GCSE Physics required practicals. Count how many waves pass a point in, say, 10 seconds to find the frequency. Freeze the pattern with a strobe or a photo next to a ruler, measure across several waves and divide by the number of waves to find the wavelength. Then multiply. Measuring across 10 waves rather than one reduces the uncertainty in each wavelength. The Practical Data Lab helps you record and analyse the results.

Common mistakes

• Not converting prefixes. kHz is × 10³, MHz is × 10⁶ and GHz is × 10⁹. Wavelengths in cm or nm must become metres.
• Mixing up period and frequency. f = 1/T. A period of 0.5 s is a frequency of 2 Hz, not 0.5 Hz.
• Measuring wavelength from crest to trough. That is only half a wavelength.
• Thinking a higher frequency means a faster wave. In the same material, the speed stays the same and the wavelength gets shorter.
• Using amplitude in the equation. Amplitude has nothing to do with wave speed.

Is the wave speed equation on the equation sheet?

Yes. AQA's GCSE Physics equations sheet, checked in November 2026, gives wave speed = frequency × wavelength, v = fλ, and period = 1 ÷ frequency, T = 1/f. AQA's A-level Physics data booklet gives c = fλ and f = 1/T in its waves section. You still need to know what each quantity means and how to measure it.

Practise waves in a short timed paper

GCSE Physics Foundation and GCSE Physics Higher each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, including waves. The Light and Energy course covers waves, the electromagnetic spectrum and photons.

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