Wave Speed Calculator
Every travelling wave obeys the wave equation v = f × λ, where v is the wave speed (metres per second), f is the frequency (hertz, or cycles per second) and λ is the wavelength (metres).
Enter Values
How to use this calculator
- Enter any two of the three values — frequency (Hz), wavelength (m) and wave speed (m/s).
- Leave the value you want to find blank; the calculator solves for it using the wave equation.
- Read off the result, including the handy km/s, kHz or cm conversion shown beneath it.
How it works
Every travelling wave obeys the wave equation v = f × λ, where v is the wave speed (metres per second), f is the frequency (hertz, or cycles per second) and λ is the wavelength (metres). Multiplying how many cycles pass each second by the length of one cycle gives how far the wave advances each second — its speed.
The same equation rearranges to find any unknown: f = v ÷ λ or λ = v ÷ f. This calculator detects which two values you entered and solves for the third exactly. The result is only as accurate as your inputs, and it assumes a single, non-dispersive wave (speed independent of frequency).
Worked example
Speed of a wave with f = 50 Hz and λ = 6 m. A wave has a frequency of 50 Hz and a wavelength of 6 m. Enter 50 in Frequency and 6 in Wavelength, and leave Wave speed blank. The calculator applies v = f × λ = 50 × 6 = 300 m/s. So the wave travels at 300 m/s (0.3 km/s).
Common mistakes
- Mixing units — the formula needs frequency in hertz, wavelength in metres and speed in metres per second. Convert kHz to Hz (×1000) and cm to m (÷100) first.
- Confusing wave speed with the speed of the medium's particles. v = f × λ gives how fast the wave pattern travels, not how fast individual particles oscillate.
- Assuming the speed changes when you change the frequency. In a given medium the speed is usually fixed, so raising the frequency shortens the wavelength — it does not speed the wave up.
Frequently asked questions
What is the formula for wave speed?
Wave speed is frequency times wavelength: v = f × λ. With frequency f in hertz and wavelength λ in metres, the speed v comes out in metres per second (m/s).
How do I find frequency or wavelength if I know the speed?
Rearrange the wave equation. To get frequency, divide speed by wavelength (f = v ÷ λ). To get wavelength, divide speed by frequency (λ = v ÷ f). Just enter the two values you know and this calculator does it for you.
Does a higher frequency mean a faster wave?
No. In a given medium the wave speed is fixed, so a higher frequency produces a shorter wavelength rather than a faster wave. The speed only changes if the medium changes — for example sound travels faster in water than in air.
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Tip: Enter any known values to calculate the remaining results.
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