Wave Speed Calculator
Use the wave equation v = fλ to solve for wave speed, frequency, or wavelength. Pick what to find, then enter the other two — frequency (Hz, kHz, MHz), wavelength (m, cm, mm, nm), or speed (m/s).
Example: with Solve for Wave speed (v) · Frequency 500 · Frequency unit Hz · Wavelength 0.686 · Wavelength unit m → Result: 343.00 m/s.
- Full set (f, λ, v)f = 500.00 Hz, λ = 0.6860 m, v = 343.00 m/s
- Comparable toAbout the speed of sound in air (343 m/s at 20 °C)
Computed by the calculator below using its default values. Change any input to see your own numbers.
The wave equation v = f × λ links speed, frequency, and wavelength. Rearranged: f = v/λ and λ = v/f. Wave speed is set by the medium; frequency comes from the source.
The one equation behind waves
Every traveling wave obeys v = fλ: its speed equals its frequency times its wavelength. Frequency is how many cycles pass a point each second, wavelength is the distance between successive crests, and their product is how fast the pattern moves. Rearranged, the same equation gives f = v/λ and λ = v/f, so any one of the three follows from the other two.
This is why a low bass note has a long wavelength and a high note a short one: in the same air they travel at the same speed, so higher frequency must mean shorter wavelength. The trade-off is fixed by the medium.
Speed is set by the medium
A wave's speed depends on what it moves through, not on its source. Sound travels about 343 m/s in room-temperature air, roughly 1,480 m/s in water, and near 5,960 m/s in steel. Light and other electromagnetic waves travel at about 3×10⁸ m/s in a vacuum — nearly a million times faster than sound in air.
When a wave crosses into a new medium its speed changes, and because the source keeps the frequency fixed, the wavelength changes to match. That is the mechanism behind refraction, why a straw looks bent in water, and how lenses focus light.
How it’s calculated
Wave equation v = f × λ. Solve for speed as v = fλ, frequency as f = v/λ, or wavelength as λ = v/f. Frequency converts at 1 kHz = 1,000 Hz and 1 MHz = 1,000,000 Hz; wavelength at 1 cm = 0.01 m, 1 mm = 0.001 m, 1 nm = 1e-9 m. Speed is in meters per second.
Assumes a single wave in a uniform, non-dispersive medium, where all frequencies travel at the same speed. In dispersive media the speed varies with frequency, and this simple relation is an approximation.
Wave speeds in different media
| Wave in medium | Typical speed | Approx. mph |
|---|---|---|
| Sound in air (20 °C) | 343 m/s | 767 mph |
| Sound in fresh water | 1,480 m/s | 3,311 mph |
| Sound in steel | 5,960 m/s | 13,332 mph |
| Light or radio in vacuum | 299,792,458 m/s | 670,616,629 mph |
Representative published values; wave speed depends on the medium and its temperature.
Common mistakes
- Forgetting to convert units — mixing kHz with meters, or nm with Hz, throws the answer off by powers of ten.
- Dividing the wrong way: frequency is speed over wavelength, not wavelength over speed.
- Assuming wave speed depends on frequency; in most everyday media it is set by the medium alone.
- Using the vacuum speed of light for a wave traveling through glass or water, where it moves slower.
Frequently asked questions
What is the wave speed formula?
Wave speed equals frequency times wavelength: v = fλ. Rearranged, frequency is v/λ and wavelength is v/f. Speed is in m/s when frequency is in hertz and wavelength in meters.
How do I find frequency from wave speed and wavelength?
Divide the speed by the wavelength: f = v/λ. For sound at 343 m/s with a 0.686 m wavelength, the frequency is 343 / 0.686 = 500 Hz.
Does wave speed depend on frequency?
Usually not. In a given medium, speed is set by the medium's properties, so raising frequency shortens wavelength to keep the product constant. Some media are dispersive, where speed does vary with frequency.
What is the speed of sound versus light?
Sound travels about 343 m/s in air, while light travels about 299,792,458 m/s in a vacuum — roughly 874,000 times faster. That gap is why you see lightning before you hear thunder.
Why does wavelength change when a wave enters a new medium?
The speed changes with the medium, but the source keeps the frequency fixed. Since v = fλ, a new speed at the same frequency forces a new wavelength, which is what bends waves during refraction.