wavelength
{{refimprove|date=November 2008}}{{Otheruses}}
thumb|320px|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.
Relationship with frequency
Wavelength
λ is determined using the formula
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: 3×10
8 m/s divided by 100×10
6 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
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
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
-
[BOOK, In Quest of the Universe, Theo Koupelis and Karl F. Kuhn, Jones & Bartlett Publishers, 2007, 0763743879,weblink ]
External links
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