Wavelength

For other uses, see Wavelength (disambiguation).
The wavelength of a sine wave, λ, can be measured between any two points with the same phase, such as between crests (on top), or troughs (on bottom), or corresponding zero crossings as shown.

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.[1][2] In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns.[3][4] The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.[5]

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.[6]

Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary. Water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary.

The range of wavelengths or frequencies for wave phenomena is called a spectrum. The name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum.

  1. ^ Hecht, Eugene (1987). Optics (2nd ed.). Addison Wesley. pp. 15–16. ISBN 0-201-11609-X.
  2. ^ Brian Hilton Flowers (2000). "§21.2 Periodic functions". An introduction to numerical methods in C++ (2nd ed.). Cambridge University Press. p. 473. ISBN 0-19-850693-7.
  3. ^ Raymond A. Serway; John W. Jewett (2006). Principles of physics (4th ed.). Cengage Learning. pp. 404, 440. ISBN 0-534-49143-X.
  4. ^ A. A. Sonin (1995). The surface physics of liquid crystals. Taylor & Francis. p. 17. ISBN 2-88124-995-7.
  5. ^ Keqian Zhang & Dejie Li (2007). Electromagnetic Theory for Microwaves and Optoelectronics. Springer. p. 533. ISBN 978-3-540-74295-1.
  6. ^ Theo Koupelis & Karl F. Kuhn (2007). In Quest of the Universe. Jones & Bartlett Publishers. p. 102. ISBN 978-0-7637-4387-1. wavelength lambda light sound frequency wave speed.