Wave Speed & Wavelength Calculator

Physics guide

The wave equation and what it tells you

Every wave, from the light entering your eyes to the sound reaching your ears to the radio signal received by your phone, obeys the same fundamental relationship. Wave speed equals frequency multiplied by wavelength. This is the most important equation in wave physics and it applies to all periodic waves regardless of their physical nature.

The fundamental wave equation

Where v is the wave speed in meters per second, f is the frequency in hertz, and lambda (the Greek letter) is the wavelength in meters. The relationship is linear and invertible: knowing any two of the three variables uniquely determines the third.

What each variable represents

• Wave speed (v): How fast the disturbance propagates through the medium. Wave speed depends on the medium, not the source. Sound travels at 343 m/s in air at 20 degrees Celsius regardless of whether it comes from a whisper or a jet engine. Light travels at 299,792,458 m/s in vacuum regardless of the source's color or brightness.
• Frequency (f): How many complete wave cycles pass a fixed point per second, measured in hertz (Hz). A frequency of 1 Hz means one cycle per second. The frequency of a wave is determined by its source and does not change when the wave moves into a different medium. What changes is the speed and therefore the wavelength.
• Wavelength (lambda): The physical distance from one point on a wave to the identical point on the next cycle, measured in meters. It is the spatial "size" of one complete oscillation. Longer wavelengths carry lower frequencies; shorter wavelengths carry higher frequencies for the same wave speed.

Electromagnetic waves

Electromagnetic waves (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays) all travel at the speed of light in vacuum: c = 299,792,458 m/s. They differ only in their frequency and wavelength. The electromagnetic spectrum spans an enormous range:

• AM radio (1 MHz): wavelength = c / f = 300 m. The antenna must be comparable in size to the wavelength, which is why AM radio towers are hundreds of meters tall.
• FM radio (100 MHz): wavelength = 3 m. A car antenna of about 75 cm (a quarter wavelength) works well.
• WiFi 2.4 GHz: wavelength = 12.5 cm. The internal antenna in a router is designed to match this scale.
• Visible light (400-700 nm): frequencies of roughly 430 to 750 THz. Red light has longer wavelengths; violet has shorter.
• X-rays (0.01-10 nm): wavelengths comparable to the spacing between atoms in a crystal, which is why crystals diffract X-rays.

Sound waves

Sound is a mechanical pressure wave that requires a medium to propagate. Its speed depends on the medium's density and elasticity, not on frequency. This is why frequency does not change at a medium boundary, but wavelength does.

A musical note at 440 Hz (concert A) has a wavelength of 343/440 = 0.780 m in air. The same note transmitted through water would have a wavelength of 1480/440 = 3.36 m, more than four times longer, because the wave travels faster but at the same frequency.

How wave speed changes with the medium

When a wave passes from one medium to another (for example, light going from air into glass), its frequency stays constant but its speed changes. The wavelength therefore also changes to maintain v = f x lambda. This is the origin of refraction: because different frequencies slow by different amounts in glass, they bend at different angles, separating white light into its component colors in a prism.

The ratio of a wave's speed in vacuum to its speed in a medium is called the refractive index (n). For glass with n = 1.5, light slows to c / 1.5 = 200,000,000 m/s, and a green photon at 550 nm in air becomes 550 / 1.5 = 367 nm inside the glass (though it appears the same color because the frequency, which determines perceived color, stays the same).

Worked examples

Sound in a concert hall. A bass note at 80 Hz in air (343 m/s):

A violin playing 3,000 Hz at the same temperature:

Visible light. Green light at 550 nm, speed = c:

Doppler effect and wave speed

The Doppler effect changes the observed frequency (and therefore perceived wavelength) when source and observer are in relative motion, but the wave speed in the medium remains the same. A police siren sounds higher in pitch as it approaches and lower as it recedes because the wavefronts are compressed (shorter wavelength, higher frequency) ahead of the moving source and stretched behind it.

Disclaimer

This calculator uses the classical wave equation and assumes non-dispersive media (wave speed independent of frequency). In dispersive media such as glass or plasma, group velocity and phase velocity differ and the simple v = f x lambda applies to the phase velocity only. Results are rounded to six significant figures.