Wavelength, frequency and speed
Every wave, whether light, radio or sound, repeats in space and in time. The wavelength is the distance between two crests; the frequency is the number of crests passing per second, in hertz. The two are tied by the speed of the wave: a wave that travels faster or oscillates more slowly has a longer wavelength.
The formulas
- Wavelength λ = v ÷ f
- Period = 1 ÷ f
- Photon energy E = h × f, with h = 4.135667696 × 10⁻¹⁵ eV·s
The calculator offers four speeds: light and radio waves in a vacuum (299,792,458 m/s, very close to their speed in air), sound in air at 20 °C (343 m/s), sound in water (1,481 m/s), or any speed you enter.
Worked example
An FM radio station broadcasts at 100 MHz.
- λ = 299,792,458 ÷ 100,000,000 = 2.998 m.
- Period: 1 ÷ 100 MHz = 10 nanoseconds.
- Each radio photon carries only 0.41 µeV, far too little to affect molecules, unlike ultraviolet light.
This is why a simple FM antenna is often about 75 cm long, a quarter of the wavelength.
The electromagnetic spectrum
| Wave | Frequency | Wavelength |
|---|---|---|
| AM radio | 1 MHz | 300 m |
| FM radio | 100 MHz | 3 m |
| Wi-Fi | 2.4 and 5 GHz | 12.5 and 6 cm |
| Microwave oven | 2.45 GHz | 12.2 cm |
| Red light | 430 THz | 700 nm |
| Violet light | 750 THz | 400 nm |
Sound waves
Sound is far slower than light, so its wavelengths are much shorter for the same frequency. In air, the musical note A at 440 Hz has a wavelength of 78 cm. The lowest note we can hear, around 20 Hz, is 17 m long, while a 20 kHz whistle is only 1.7 cm. That explains why bass passes through walls and around obstacles more easily than treble.
Photon energy
Light and radio waves come in packets called photons, whose energy is proportional to frequency. Visible light carries about 1.7 to 3.1 eV per photon, enough to trigger chemical reactions in the retina or in a plant leaf. Ultraviolet photons, above about 3.1 eV, can damage DNA, which is why sunscreen matters, while radio photons, millions of times weaker, cannot.
A note on media
Light slows down in glass or water, so its wavelength shrinks there while its frequency stays the same. That change of speed is what causes refraction, covered by the Snell’s law calculator.