Every wave — light, radio, sound — obeys one tidy relationship: it travels exactly one wavelength in one cycle, so its speed equals its frequency times its wavelength, v = f·λ. Rearranged, the wavelength is just the speed divided by the frequency. Because the speed is fixed (the speed of light for anything electromagnetic, ~343 m/s for sound in air), frequency and wavelength are locked together inversely: crank the frequency up and the wavelength shrinks. That single equation sizes antennas, explains colour, and underpins all of spectroscopy.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the wave equation v = fλ.
The wave equations
For electromagnetic waves the speed is the speed of light, c ≈ 2.998×10⁸ m/s in vacuum; for sound use the medium's speed (≈343 m/s in air). The period is simply the inverse of frequency, and a wave advances one wavelength per period. For light, multiplying the frequency by Planck's constant gives the energy carried by each photon — which is why high-frequency, short-wavelength radiation like UV and X-rays is far more energetic than radio.
Worked example — an FM radio wave
Scenario: An FM station broadcasts at 100 MHz. What is its wavelength and period?
The 100 MHz wave is about 3 m long, which is why FM aerials are sized in metres — a quarter-wave whip is roughly 0.75 m. Its period is 10 nanoseconds. Push the frequency up to 2.4 GHz for Wi-Fi and the wavelength collapses to about 12.5 cm, so the antenna inside a router can be tiny. At the other extreme, visible light near 5×10¹⁴ Hz has a wavelength of only ~600 nm — a thousandth the width of a hair.
Frequently Asked Questions
λ = v/f. For light (3×10⁸ m/s), 100 MHz → 3 m. For sound use v ≈ 343 m/s.
v = f × λ — speed equals frequency times wavelength. Rearrange for λ or f.
λ = v/f. 2.4 GHz Wi-Fi → ~12.5 cm; 5×10¹⁴ Hz light → ~600 nm. Higher f = shorter λ.
Yes — slower medium, shorter wavelength (frequency unchanged). Light in glass ≈ vacuum λ ÷ n.
T = 1/f, and λ = v·T. A wave covers one wavelength each period. 100 MHz → T 10 ns, λ 3 m.