Wavelength

Wavelength of a sine wave.

In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek letter lambda (λ). Examples of wave-like phenomena are light, water waves, and sound waves. The wavelength is related to the frequency by the formula: wavelength = wave speed / frequency. Wavelength is therefore inversely proportional to frequency. Higher frequencies have shorter wavelengths. Lower frequencies have longer wavelengths, assuming the speed of the wave is the same.[1]

In a wave, properties vary with position. For example, in a sound wave the air pressure oscillates, while in light and other electromagnetic radiation the strength of the electric and the magnetic field vary.

Visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (430–750 THz). For other examples, see electromagnetic spectrum. The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are between approximately 17 m and 17 mm, respectively, assuming a typical speed of sound of about 340 m/s; the wavelengths in audible sound are much longer than those in visible light.

Contents

Relationship with frequency

Wavelength λ is determined using the formula

\lambda = \frac{v}{f},

where v is the phase speed of the wave and f is its frequency. In the case of electromagnetic radiation, such as light, in a vacuum, this speed is the speed of light, 299,792,458 m/s or about 3×108 m/s. For sound waves in air, this is the speed of sound, 345 m/s (1238 km/h) in air at room temperature and atmospheric pressure. Usually, SI units are used, where the wavelength is expressed in metres, the frequency in Hz, and the propagation speed is in metres per second.

For example, the wavelength for a 100 MHz electromagnetic (radio) wave is about: 3×108 m/s divided by 100×106 Hz = 3 metres. Electronic engineers often use a shortcut formula: wavelength λ in metres = 300 Mm/s divided by the frequency in MHz, to avoid counting the (many) zero digits in the decimal or scientific notations.

It should be noted that for many wave phenomena, wavelength is not the distance that particles travel during a period. For instance, in acoustics and water waves, the particle displacements during a period are only a small fraction of the wavelength, apart from extreme conditions like breaking waves and shock waves.

It should also be noted that frequency and wavelength can change independently, but only when the speed of the wave changes. For example, when light enters another medium, its speed and wavelength change while its frequency does not.

In non-vacuum media

The speed of light in most media is lower than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum. The wavelength in the medium is

\lambda'=\frac{\lambda_0}{n},

where n is the refractive index of the medium. Wavelengths of electromagnetic radiation are usually quoted in terms of the vacuum wavelength, unless specifically indicated as the "wavelength in the medium". In acoustics, where a medium is essential for the waves to exist, the term wavelength is always the wavelength in the medium. Then the refractive index depends on the mean properties of the medium, for instance the mean pressure or changes in the material composition.

De Broglie wavelength of particles

Louis de Broglie postulated that all particles with momentum have a wavelength

\lambda = \frac{h}{p},

where h is Planck's constant, and p is the momentum of the particle. This hypothesis was at the basis of quantum mechanics. Nowadays, this wavelength is called the de Broglie wavelength. For example, the electrons in a CRT display have a De Broglie wavelength of about 10-13 m.

See also

References

  1. ↑ Theo Koupelis and Karl F. Kuhn (2007). In Quest of the Universe. Jones & Bartlett Publishers. ISBN 0763743879. http://books.google.com/books?id=WwKjznJ9Kq0C&pg=PA102&dq=wavelength+lambda+light+sound+frequency+wave+speed&lr=&as_brr=3&ei=nfIpSazAMIzukgSP04nODg. 

External links