What is the wave speed formula?

The wave speed formula is v = f times lambda, where v is the wave speed in metres per second, f is the frequency in hertz (cycles per second), and lambda is the wavelength in metres. It can be rearranged to find any of the three variables: f = v divided by lambda, or lambda = v divided by f. The period T is the reciprocal of frequency: T = 1 divided by f.

What is the speed of sound in air?

At 20 degrees Celsius, the speed of sound in dry air is approximately 343 m/s (about 1235 km/h). It increases with temperature at roughly 0.6 m/s per degree Celsius. The speed of sound is much lower in air than in water (about 1480 m/s) or steel (about 5000 m/s), because gases are less stiff than liquids or solids.

Why does wave speed stay constant while frequency changes?

The speed of a wave through a given medium is determined by the properties of that medium (density, elasticity, or for light, permittivity and permeability). It does not change when the frequency changes. Instead, when a wave moves from one medium to another, its frequency stays constant (because the source is unchanged) but its wavelength changes to match the new speed: lambda = v divided by f. This is why light bends (refracts) when it enters glass: its speed and wavelength change while its frequency stays the same.

Wave Speed Calculator

All waves, whether they are sound waves, light waves, water waves, or seismic waves, share a fundamental relationship between speed, frequency, and wavelength. The wave speed v equals the frequency f multiplied by the wavelength lambda: v equals f times lambda. Frequency measures how many complete cycles pass a fixed point every second, measured in hertz. Wavelength is the distance between two successive crests (or troughs, or any identical points on consecutive cycles), measured in metres. The product of these two quantities gives the speed at which the wave propagates through its medium. This equation can be rearranged to solve for any of the three variables: frequency equals speed divided by wavelength, and wavelength equals speed divided by frequency. The speed of a wave in a given medium is determined by the physical properties of that medium. Sound travels at about 343 m/s through dry air at 20 degrees Celsius, about 1480 m/s through water, and about 5000 m/s through steel. Light travels at approximately 3 times 10 to the power of 8 m/s in a vacuum (the cosmic speed limit), and somewhat slower in glass or water. This calculator lets you solve for wave speed, frequency, or wavelength. You enter any two of the three values and choose which to solve for. A selection of common medium presets fills in the speed for you. Supporting outputs include the wave period, wavenumber, and angular frequency.

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Solve for

Medium preset

Wave speed v

m/s

Frequency f

Wavelength λ

0.780 m

solved variable

Period T = 1/f0.002273 s

Wavenumber k8.055 rad/m

Angular freq. ω2765 rad/s

Wave speed depends on the medium. Changing frequency does not change wave speed; it changes the wavelength instead.

How it works

The wave equation is v = f × λ. Rearranging: f = v / λ; λ = v / f. Period T = 1 / f in seconds. Wavenumber k = 2π / λ in rad/m. Angular frequency ω = 2πf in rad/s. Select which variable to solve for, enter the other two, and the calculator returns the missing value along with the supporting wave properties.

Worked example

The musical note A4 has a frequency f = 440 Hz. Sound travels at approximately 343.2 m/s in air at 20 °C. Using λ = v / f: λ = 343.2 / 440 = 0.780 m. Period T = 1/440 = 0.002273 s. Angular frequency ω = 2π × 440 = 2765 rad/s. These match the default values pre-filled in the calculator above.

Related calculators

Doppler Effect Calculator: find the observed frequency when a source or observer is moving.
Snell's Law Calculator: calculate how waves bend when crossing between media.
Velocity Calculator: solve for speed, distance, or time in linear motion.
Percent Error Calculator: compare a measured wave speed to a theoretical value.

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