Wave speed equation: v = fλ
Wave speed = frequency × wavelength. In symbols, v = f λ. v is the wave speed in metres per second (m/s), f is the frequency in hertz (Hz) and λ (the Greek letter lambda) is the wavelength in metres (m). All six GCSE physics specifications from AQA, Edexcel and OCR include it, and the sheet in your exam paper prints it.
Equation
v = f λ
| Symbol | Quantity | Unit |
|---|---|---|
v | speed | m/s |
f | frequency | Hz |
λ | wavelength | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | v = f λ |
| AQA Combined Science (8464) | Recall | v = f λ |
| Edexcel Physics (1PH0) | Recall | v = f λ |
| Edexcel Combined Science (1SC0) | Recall | v = f λ |
| OCR Gateway Physics A (J249) | Recall | v = f λ |
| OCR Twenty First Century Physics B (J259) | Recall | v = f λ |
Calculator: v = f λ
Equation
v = s ÷ t
| Symbol | Quantity | Unit |
|---|---|---|
v | wave speed | m/s |
s | distance | m |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Not in this specification | |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Recall | v = x/t |
| Edexcel Combined Science (1SC0) | Recall | v = x/t |
| OCR Gateway Physics A (J249) | Not in this specification | |
| OCR Twenty First Century Physics B (J259) | Not in this specification |
Calculator: v = s ÷ t
Equation
T = 1 ÷ f
| Symbol | Quantity | Unit |
|---|---|---|
T | period | s |
f | frequency | Hz |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet | T = 1/f |
| AQA Combined Science (8464) | Given on the sheet | T = 1/f |
| Edexcel Physics (1PH0) | Not in this specification | |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Not in this specification | |
| OCR Twenty First Century Physics B (J259) | Not in this specification |
Calculator: T = 1 ÷ f
Frequency, wavelength and speed
Frequency is how many waves pass a point each second. One hertz means one wave per second. Wavelength is the distance from one crest to the next crest. A crest is the top of a wave.
Picture waves hitting a beach. If four waves arrive each second and they are 2 m apart, the wave pattern moves forward 8 m every second. That is the whole idea behind v = f λ.
The material a wave travels through sets its speed. Sound moves faster in water than in air, and light slows down in glass. In one material, a higher frequency gives a shorter wavelength, and the speed stays the same.
How the boards print it
Every board prints v = f λ in the same way. AQA (8463 and 8464), Edexcel (1PH0 and 1SC0) and OCR (J249 and J259) put it on the recall list in their specifications. Since 2025 every equation on those lists also appears on the exam sheet.
Edexcel adds a second wave speed equation: wave speed = distance ÷ time, v = x/t. It is the same idea as the speed equation, used for a wave. You can see both on the Edexcel equation list.
AQA also gives period = 1 ÷ frequency, T = 1/f, among its given equations. The period is the time for one whole wave to pass. The AQA page shows where it sits.
Rearranged forms
- f = v ÷ λ
- λ = v ÷ f
To find a frequency, divide the speed by the wavelength. To find a wavelength, divide the speed by the frequency. Sound in air travels at roughly 340 m/s, so a low note of 85 Hz has waves about 4 m long. A high whistle at 3400 Hz has waves only 10 cm long.
Every wave question on this topic needs one multiplication or one division. The skill is in the units, so turn centimetres into metres and kilohertz into hertz before you start. The full list of wave and other equations is on the physics equation sheet page.
Worked examples
v
- Change the wavelength to metres: 2.5 cm = 0.025 m
- v = f λ
- v = 12 × 0.025
- v = 0.3 m/s
0.3 m/s
λ
- λ = v ÷ f
- λ = 340 ÷ 170
- λ = 2 m
2 m
f
- f = v ÷ λ
- f = 1500 ÷ 0.75
- f = 2000 Hz
2000 Hz
Common mistakes
- Leaving a ripple tank wavelength in centimetres. The speed then comes out 100 times too big for m/s.
- Forgetting that kHz means thousands. A 3 kHz sound has a frequency of 3000 Hz.
- Measuring wavelength from a crest to the next trough. That is only half a wave, so your λ is half the real value.
- Thinking a higher pitch makes sound travel faster. The speed depends on the material, so the wavelength changes instead.
Make f or λ the subject of v = fλ in the Equation Rearranger.
Questions people ask
What is the symbol λ?
It is lambda, a Greek letter. Physics uses it for wavelength, measured in metres.
Does v = fλ work for light?
Yes. It works for every wave, including light, sound, radio and water waves. Light in air moves at about 300 000 000 m/s, so its wavelengths are tiny.