Quick answer
This wave speed calculator uses the wave equation v = fλ. Enter any two of speed, frequency and wavelength to find the third. It also gives the period, T = 1/f. It works for sound, light, water waves and waves on strings.
Wave speed, frequency and wavelength (v = fλ)
How to Use the Wave Speed Calculator
- Choose speed, frequency or wavelength.
- Enter the other two values: speed in m/s, frequency in Hz and wavelength in metres.
- Press Calculate.
Tip: Convert first: 100 MHz = 1 × 10⁸ Hz, 500 nm = 5 × 10⁻⁷ m and 2 cm = 0.02 m. You can type 1e8 for 1 × 10⁸.
The Wave Equation
v = fλ
v is wave speed (m/s), f is frequency (Hz) and λ is wavelength (m). The medium sets the wave speed, so in one medium a higher frequency means a shorter wavelength.
| Wave | Typical speed |
|---|---|
| Sound in air (20 °C) | about 343 m/s |
| Sound in water | about 1,480 m/s |
| Light in a vacuum | 299,792,458 m/s |
See how the wave equation fits into wave physics in our waves and optics guide.
Worked Example
Worked example: a musical note
Question: The note A above middle C has a frequency of 440 Hz. What is its wavelength in air, where sound travels at 343 m/s?
- Choose “Wavelength (λ)”.
- λ = v ÷ f = 343 ÷ 440.
- λ ≈ 0.78 m.
Answer: The wavelength is about 0.78 m.
Learn more: explore transverse waves with labelled diagrams and real-life examples.
Frequently Asked Questions
What is the formula for wave speed?
Wave speed equals frequency multiplied by wavelength: v = fλ.
Does frequency change when a wave enters a new medium?
No. The frequency is set by the source and stays the same. The speed and wavelength change together.
How do I find the period of a wave?
The period is the reciprocal of the frequency: T = 1 ÷ f. A 50 Hz wave has a period of 0.02 s.