Wavelength, speed and frequency are one equation
Wavelength is the distance between two crests of a wave. It equals the wave’s speed divided by its frequency, so at a fixed speed the two are inversely proportional: double the frequency and the wavelength halves. For light in a vacuum, v is the speed of light, exactly 299,792,458 m/s. Rearranged, f = v ÷ λ and v = λ × f.
The electromagnetic spectrum by wavelength
| Band | Wavelength | Frequency |
|---|---|---|
| Radio | > 1 mm | < 300 GHz |
| Microwave | 1 mm – 1 µm | 0.3 – 300 THz |
| Infrared | 1 µm – 700 nm | 300 – 430 THz |
| Visible | 700 – 380 nm | 430 – 790 THz |
| Ultraviolet | 380 – 10 nm | 0.79 – 30 PHz |
| X-ray | 10 – 0.01 nm | 30 PHz – 30 EHz |
| Gamma | < 0.01 nm | > 30 EHz |
Shorter wavelength means higher frequency and higher photon energy (E = hc ÷ λ), which is why UV and X-rays are ionising while radio waves are not.
The visible band in more detail
| Colour | Wavelength |
|---|---|
| Red | 620 – 750 nm |
| Orange | 590 – 620 nm |
| Yellow | 560 – 590 nm |
| Green | 490 – 560 nm |
| Blue | 450 – 495 nm |
| Violet | 380 – 450 nm |
Where the wave speed comes from
- Vacuum. Light travels at c = 299,792,458 m/s, close enough to 3 × 108 for quick work.
- A medium slows it. Speed in a material is c ÷ n, where n is the refractive index: 1.33 for water, 1.5 for glass, 2.42 for diamond.
- Sound is not light. Sound in air moves at about 343 m/s, so a 1 kHz tone has a wavelength near 0.34 m, not a light wavelength. Use the speed that matches the wave.
Common questions
How do you calculate wavelength from frequency?
Divide the wave speed by the frequency. For light in a vacuum that speed is 299,792,458 metres per second, so a 5 x 10^14 Hz wave has a wavelength of about 600 nm (orange light).
What is the wavelength of visible light?
Roughly 380 to 700 nanometres. Violet sits at the short end near 380 nm and red at the long end near 700 nm. The eye is most sensitive to green, around 555 nm.
Does wavelength change in water or glass?
Yes. Light slows down in a denser medium while its frequency stays fixed, so the wavelength shrinks. In water it drops to about three quarters of its vacuum value.
