Key takeaways
- Wave speed is v = f × λ: frequency times wavelength, in metres per second.
- Frequency counts cycles per second (Hz); wavelength measures a physical length (m).
- For a fixed wave speed, higher frequency means shorter wavelength, not a faster wave.
- Sound in air travels at roughly 343 m/s regardless of its pitch.
In this guide
What is wave speed?
Wave speed is how fast a wave pattern travels through a medium, such as sound through air or ripples across water. It depends on how often the wave repeats (frequency) and how long each repeat is (wavelength).
Why does wave speed matter?
Wave speed connects two things you can measure separately, frequency and wavelength, into the number that actually describes how fast the wave itself travels.
A 500 Hz sound wave with a wavelength of 0.68 m travels at about 340 m/s, very close to the real speed of sound in air, which is roughly 343 m/s at room temperature.
The formula
| Symbol | What it means | Example |
|---|---|---|
| v | The wave speed, in metres per second (m/s) | 340 m/s |
| f | The frequency, in hertz (Hz) | 500 Hz |
| λ | The wavelength, in metres (m) | 0.68 m |
How to calculate wave speed step by step
- 1Find the frequency. Measure it in hertz.
- 2Find the wavelength. Measure it in metres.
- 3Multiply frequency by wavelength.
f × λgives you the wave speed. - 4Write the answer in metres per second.
Try the calculator below with your own frequency and wavelength to see every step worked out.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Wrong wavelength units. Wavelength must be in metres, so convert from centimetres or nanometres first if needed.
- Assuming all waves travel at the same speed. Different waves (sound, light, water waves) travel at very different speeds through the same medium.
- Forgetting the wave speed can change. Sound travels faster through water than through air, so this calculator's speed depends on the medium.
Tips and tricks
- To estimate quickly, round frequency and wavelength to easy numbers before multiplying.
- Working backwards from speed to wavelength? Divide by frequency:
λ = v ÷ f. - Wave speed depends on the medium: sound travels faster through denser materials like water than through air, a property tied to the material's density.
- Combined with the velocity formula, wave speed is a core tool for describing anything that moves in repeating patterns.
Where you'll use it in real life
- Sound and music: instrument tuning and acoustics rely on the relationship between frequency, wavelength, and speed.
- Radio: radio stations are tuned to specific frequencies, each with a matching wavelength for a given wave speed.
- Earthquakes: seismologists use wave speed through rock to study earthquakes and locate their origin.
- Water waves: the same formula explains how ocean or pool waves relate their spacing to how fast they travel.
Quick summary
To find wave speed, multiply the frequency in hertz by the wavelength in metres. It's the same idea for sound, light, or water, even though each travels at a very different speed. Use the calculator above to check your own numbers.
Worked example
A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m in air. What is its wave speed?
- 01v = f × λ
- 02v = 500 × 0.68
- 03v = 340 m/s
These numbers are pre-filled in the calculator above.
Frequently asked questions
How do I calculate wave speed?
Multiply the frequency in hertz by the wavelength in metres: v = f × λ. The result is in metres per second.
What is the speed of sound in air?
About 343 m/s at room temperature, though it changes slightly with temperature and the medium the sound travels through.
What's the difference between frequency and wavelength?
Frequency is how many wave cycles occur per second (Hz). Wavelength is the physical length of one full cycle (m). Multiplying them gives speed.
Does a higher frequency mean a faster wave?
Not necessarily. For a fixed wave speed, like sound in air, a higher frequency actually means a shorter wavelength, not a faster wave.
