A wavetrain (denoted by some variable X) can be regarded as a one-parameter family of such hypersurfaces in spacetime. k The Lorentz matrix is defined as, In the situation where light is being emitted by a fast moving source and one would like to know the frequency of light detected in an earth (lab) frame, we would apply the Lorentz transformation as follows. {\displaystyle T} is the temporal component, and the wavenumber vector [1] For this article, they will be called the "physics definition" and the "crystallography definition", respectively. λ A perfect one-dimensional traveling wave follows the equation: k is the magnitude of the wave vector. 0 Like any vector, it has a magnitude and direction, both of which are important. There are two common definitions of wave vector, which differ by a factor of 2π in their magnitudes. ), this becomes: To apply this to a situation where the source is moving straight towards the observer ( 0.87 nm. k = where the photon energy was multiplied with the electronic charge to convert the energy in Joule rather than electron Volt. k {\displaystyle v_{p}} Conversion factors for energy equivalents For your convenience, you may convert energies online below. {\displaystyle \lambda } ω When written out explicitly its contravariant and covariant forms are: In general, the Lorentz scalar magnitude of the wave four-vector is: The four-wavevector is null for massless (photonic) particles, where the rest mass divided by the phase-velocity {\displaystyle k^{1}} In other words, it’s the distance over which the shape of the wave repeats. component results in, where k = 7.63 x 10-25 kg m/s. the energy in Joule rather than electron Volt. {\displaystyle {\frac {\omega }{c}}} = which would have the following relation between the frequency and the magnitude of the spatial part of the four-wavevector: The four-wavevector is related to the four-momentum as follows: The four-wavevector is related to the four-frequency as follows: The four-wavevector is related to the four-velocity as follows: Taking the Lorentz transformation of the four-wavevector is one way to derive the relativistic Doppler effect. T {\displaystyle k} k As an example, to apply this to a situation where the source is moving directly away from the observer ( . wrt {\displaystyle \theta =\pi /2} In crystallography, the same waves are described using slightly different equations. {\displaystyle kx} k If the medium is anisotropic, the wave vector in general points in directions other than that of the wave propagation. [2] In one and three dimensions respectively: The differences between the above two definitions are: The direction of k is discussed in the next section. r Alternately, the wavenumber m 108/(1.6 x 10-19 x 2) = 621 nm. = In the context of special relativity the wave vector can also be defined as a four-vector. where the photon energy was multiplied with the electronic charge to convert {\displaystyle \omega /k} = c → , For example, when a wave travels through an anisotropic medium, such as light waves through an asymmetric crystal or sound waves through a sedimentary rock, the wave vector may not point exactly in the direction of wave propagation. The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates, as: where the angular frequency The derivative of this scalar is a vector that characterizes the wave, the four-wavevector.[6]. / 0 θ v One definition is preferred in physics and related fields, while the other definition is preferred in crystallography and related fields. The wave vector is always perpendicular to surfaces of constant phase. You can use the photon energy calculator to further explore the relationship between the photon energy and its frequency or wavelength. 0 ; the direction of the wave vector is discussed in the following section. μ This variable X is a scalar function of position in spacetime. c = π can be written as the angular frequency / is the direction cosine of There are two common definitions of wave vector, which differ by a … θ In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. {\displaystyle k^{0},k^{1}=k^{0}\cos \theta .}. The energy of a single photon is a small number because the Planck constant is ridiculously tiny. , representing the wave vector and the position vector, respectively. {\displaystyle {\vec {k}}} {\displaystyle \theta =\pi } o In a homogeneous wave, the surfaces of constant phase are also surfaces of constant amplitude. The parameters frequency, wavelength, and speed are quantities that can be used to describe a wave. OR enter the 2 {\displaystyle v_{p}=c}. p ω x The condition for the wave vector to point in the same direction in which the wave propagates is that the wave has to be homogeneous, which isn't necessarily satisfied when the medium is anisotropic. 1.6 x 10-19 x 2)1/2 Wavelength refers to a periodic wave’s spatial period. k 6.625 x 10-34 / 7.63 x 10-25 = 1 0 {\displaystyle \theta =0}

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