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.
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.
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