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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.
It equals the spatial frequency. For example, a wavenumber in inverse centimeters can be converted to a frequency expressed in the unit gigahertz by multiplying by 29.979 2458 cm/ns (the speed of light, in centimeters per nanosecond); [5] conversely, an electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space.
The frequency and the period are related by the equation [4] =. ... (c in vacuum or less in other media), f is the frequency and λ is the wavelength.
where the angular frequency is the temporal component, and the wavenumber vector is the spatial component. Alternately, the wavenumber k can be written as the angular frequency ω divided by the phase-velocity v p, or in terms of inverse period T and inverse wavelength λ.
The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.
The de Broglie wavelength is the wavelength, λ, associated with a particle with momentum p through the Planck constant, h: =. Wave-like behavior of matter has been experimentally demonstrated, first for electrons in 1927 and for other elementary particles , neutral atoms and molecules in the years since.
Photon energy is directly proportional to frequency. [1] = where is energy (joules in the SI system) [2] is the Planck constant; is frequency [2] This equation is known as the Planck relation. Additionally, using equation f = c/λ, = where
Phase comparison is a comparison of the phase of two waveforms, usually of the same nominal frequency. In time and frequency, the purpose of a phase comparison is generally to determine the frequency offset (difference between signal cycles) with respect to a reference. [3]