frequency

Frequency is the number of recurrences of something per unit time, e.g., cycles of something repeating, such as repeating waves. The common unit of frequency, hertz is defined as the number of cycles/recurrences per second. In astrophysics, a very common use of the term frequency is in relation to electromagnetic radiation (EMR) for the rate at which individual waves are sent or received. For such a traveling wave, the wavelength times the frequency is the wave speed:

s = λ × ν

• s - the speed (for EMR, the speed of light, c):
• λ - the wavelength.
• ν - the frequency.

The energy of a photon (photon energy) is directly related to its EMR frequency:

E = h × ν

• E - energy of photon.
• h - Planck constant.
• ν - frequency.

Frequency, wavelength, and photon energy offer three means of quantifying the same characteristic of EMR: frequency is often cited for the longest wavelengths (radio, and sometimes for microwave), and photon energy for the shortest (X-rays and gamma rays), with wavelength commonly used for visible light and the surrounding regions of the spectrum.

The term frequency is also used for other types of waves such as gravitational waves and acoustic/sound waves and other cycling astronomical phenomena such as regularly pulsing radiation (e.g., from pulsars). In general, the reciprocal of the frequency is the period (wave period, for the frequency of a repeating wave), a length of time.

The term angular frequency (typically symbolized ω) is the frequency multiplied by 2π. If a cycle is thought of as motion around a circle, this product is the number of radians traversed per unit time. It can be thought of as a shorthand, and enough physical formulas use this product to make it a convenient value.

The term spatial frequency (aka wavenumber, for traveling waves) is the number of occurrences per unit distance rather than per unit time, e.g., "how many waves are there at some point in time over the course of a meter", which can be specified in units of 1/m.