Waves are everywhere — sound, radio, light, even ripples on water. Two numbers describe any of them: how often the wave cycles past you (frequency) and how long each cycle stretches in space (wavelength). The two are tied together by the wave's speed, and that single equation, c = f × λ, unlocks a huge part of physics.
The Electromagnetic Spectrum
| Band | Frequency | Wavelength | Everyday Example |
|---|---|---|---|
| Radio | 3 Hz – 300 GHz | 1 mm – 100,000 km | AM/FM, TV, Wi-Fi |
| Microwave | 300 MHz – 300 GHz | 1 mm – 1 m | Microwave oven, radar, 5G |
| Infrared | 300 GHz – 430 THz | 700 nm – 1 mm | Remote controls, heat lamps |
| Visible | 430–750 THz | 400–700 nm | Light you can see |
| Ultraviolet | 750 THz – 30 PHz | 10–400 nm | Sunburn, sterilisation |
| X-ray / Gamma | > 30 PHz | < 10 nm | Medical imaging, nuclear |
The Wave Equation in Practice
For electromagnetic waves in vacuum, c ≈ 299,792,458 m/s. So a Wi-Fi signal at 2.4 GHz has a wavelength of c/f ≈ 0.125 m — about 12.5 cm. A 100 MHz FM radio station has a wavelength of 3 m, which is why FM antennas are roughly that size. Green light at 550 nm corresponds to a frequency of c/λ ≈ 5.45 × 10¹⁴ Hz, or 545 THz.
For sound, the wave speed is about 343 m/s in air at 20 °C. Middle A (440 Hz) has a wavelength of 0.78 m. A 20 kHz tone — the upper edge of human hearing — sits at 1.7 cm, which is why tiny earbuds can still reproduce high frequencies cleanly while needing larger drivers for bass.
Useful Conversions
- 1 kHz = 10³ Hz; 1 MHz = 10⁶ Hz; 1 GHz = 10⁹ Hz; 1 THz = 10¹² Hz.
- Vacuum wavelength (m) = 3 × 10⁸ ÷ frequency (Hz).
- 1 nm = 10⁻⁹ m; visible light is 400–700 nm.
- Photon energy (eV) ≈ 1240 ÷ wavelength (nm).
A Reliable Method for Any Wave Problem
Whatever the wave — radio, light, or sound — the same short routine prevents the usual factor-of-1000 slips:
- Pick the right speed. Use c = 3 × 10⁸ m/s for electromagnetic waves in vacuum, or about 343 m/s for sound in air. Mixing the two is the classic error.
- Convert everything to base SI units first. Turn GHz into Hz and nm into metres before dividing, so the powers of ten line up.
- Apply λ = c / f (or f = c / λ). Example: a 5 GHz Wi-Fi signal → 3 × 10⁸ ÷ 5 × 10⁹ = 0.06 m, about 6 cm.
- Sanity-check the scale. Higher frequency must give a shorter wavelength; if it doesn't, you have an exponent flipped.
Convert Distance Units
Wavelengths span nanometres to kilometres — UnitSnap's length converter handles them all.
Length Converter →