Wavelength
Wavelength is the spatial distance between two consecutive points that are in the same phase of a wave, such as crest to crest or trough to trough. It is denoted by the Greek letter lambda (λ) and measured in metres. Wavelength is inversely related to frequency: higher-frequency waves have shorter wavelengths, which is why X-rays (short λ) are more energetic than radio waves (long λ).
Key Formula
lambda = v / f
LaTeX: \lambda = \dfrac{v}{f}
| Symbol | Meaning | Unit |
|---|---|---|
| λ | Wavelength | m |
| v | Wave speed | m/s |
| f | Frequency | Hz |
Worked Example
Problem
A sound wave travels through air at 340 m/s with a frequency of 680 Hz. What is its wavelength?
Solution
Step 1: Write the formula — λ = v / f. Step 2: Substitute values — λ = 340 m/s ÷ 680 Hz. Step 3: Calculate — λ = 0.5 m.
Answer
λ = 0.5 m
Wavelengths of Different Regions of the Electromagnetic Spectrum
| Region | Wavelength Range | Frequency Range | Common Use |
|---|---|---|---|
| Radio waves | > 1 m | < 300 MHz | Broadcasting |
| Microwaves | 1 mm – 1 m | 300 MHz – 300 GHz | Radar, cooking |
| Infrared | 700 nm – 1 mm | 300 GHz – 430 THz | Thermal imaging |
| Visible light | 400 – 700 nm | 430 – 750 THz | Human vision |
| Ultraviolet | 10 – 400 nm | 750 THz – 30 PHz | Sterilisation |
| X-rays | 0.01 – 10 nm | 30 PHz – 30 EHz | Medical imaging |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Wave
A wave is a disturbance that transfers energy through a medium or through space without permanently displacing the medium itself. Waves are fundamental to how energy propagates in nature, from ocean ripples to light traveling across the universe. They are characterised by properties such as wavelength, frequency, amplitude, and speed, and underpin technologies ranging from radio communication to medical ultrasound.
Frequency
Frequency is the number of complete wave cycles that pass a fixed point per unit time, measured in hertz (Hz), where 1 Hz equals one cycle per second. It determines the pitch of a sound (higher frequency = higher pitch) and the colour of light (higher frequency = more energetic, bluer light). Frequency is inversely proportional to the wave period: f = 1/T.
Period (wave)
The period of a wave is the time taken for one complete wave cycle to pass a fixed point, measured in seconds. It is the reciprocal of frequency: T = 1/f. Period is important in analysing oscillating systems such as pendulums, AC circuits, and vibrating strings, where knowing the cycle time allows calculation of frequency and wave speed.
A compound of "wave" and "length," first used in the 19th century as physicists began quantifying wave properties. The symbol λ (lambda) was adopted from the Greek alphabet in the same era.