Angular frequency in the context of "Turn (unit)"

The Planck relation (referred to as Planck's energy–frequency relation, the Planck–Einstein relation, Planck equation, and Planck formula, though the latter might also refer to Planck's law) is a fundamental equation in quantum mechanics which states that the photon energy E is proportional to the photon frequency ν (or f):$${\displaystyle E=h\nu =hf.}$$The constant of proportionality, h, is known as the Planck constant. Several equivalent forms of the relation exist, including in terms of angular frequency ω:$${\displaystyle E=\hbar \omega ,}$$where the reduced Planck constant is ${\displaystyle \hbar =h/2\pi }$.

The relation accounts for the quantized nature of light and plays a key role in understanding phenomena such as the photoelectric effect and black-body radiation (where the related Planck postulate can be used to derive Planck's law).

In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the inverse of a band-pass filter. A notch filter is a band-stop filter with a narrow stopband (high Q factor).

Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin, bass instrument amplifier, etc.) to reduce or prevent audio feedback, while having little noticeable effect on the rest of the frequency spectrum (electronic or software filters). Other names include "band limit filter", "T-notch filter", "band-elimination filter", and "band-reject filter".

Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis.Its SI unit is the reciprocal seconds (s); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).

Rotational frequency can be obtained dividing angular frequency, ω, by a full turn (2π radians): ν=ω/(2π rad).It can also be formulated as the instantaneous rate of change of the number of rotations, N, with respect to time, t: n=dN/dt (as per International System of Quantities).Similar to ordinary period, the reciprocal of rotational frequency is the rotation period or period of rotation, T=ν=n, with dimension of time (SI unit seconds).

In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the ordinary frequency, defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the angular frequency, defined as the phase angle divided by time (in radians per second).

In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.

In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. The table of spherical harmonics contains a list of common spherical harmonics.

Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, certain functions defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3).

In acoustics, Stokes's law of sound attenuation is a formula for the attenuation of sound in a Newtonian fluid, such as water or air, due to the fluid's viscosity. It states that the amplitude of a plane wave decreases exponentially with distance traveled, at a rate α given by$${\displaystyle \alpha ={\frac {2\eta \omega ^{2}}{3\rho V^{3}}}}$$where η is the dynamic viscosity coefficient of the fluid, ω is the sound's angular frequency, ρ is the fluid density, and V is the speed of sound in the medium.

The law and its derivation were published in 1845 by the Anglo-Irish physicist G. G. Stokes, who also developed Stokes's law for the friction force in fluid motion. A generalisation of Stokes attenuation taking into account the effect of thermal conductivity was proposed by the German physicist Gustav Kirchhoff in 1868.