Frequency

Frequencies redirects here. For other uses, see Frequencies (film), Frequencies (album), and Frequency (disambiguation).

Frequency is how often something happens in a given amount of time. It helps us understand how quickly events repeat themselves. Scientists and engineers use frequency to describe many things, like how fast a heart beats, how a guitar string vibrates, or how quickly radio waves move.

The time between each event is called the period. If something happens very often, its period is short. For example, if a heart beats 120 times in one minute, the period between beats is half a second.

There are special ways to talk about frequency in different situations. Angular frequency looks at how fast something spins or moves in circles. Spatial frequency looks at how often patterns repeat in space, like the lines on a brick wall.

The unit for measuring frequency is the hertz, written as Hz. One hertz means one event happens every second.

Definitions and units

For repeating events like oscillations, waves, or simple back-and-forth motion, frequency means how many times something happens in a given time. We often use the letter f or the Greek letter ν (nu) to stand for frequency. The period is the time it takes for one full cycle to happen. Frequency and period are connected by the simple rule: frequency equals one divided by the period.

The official unit for measuring frequency is the hertz (Hz), named after the scientist Heinrich Hertz. It tells us how many cycles happen each second. Before 1960, people used to say "cycles per second" instead of hertz. For measuring how fast something spins, we sometimes use revolutions per minute (rpm). Sixty rpm equals one hertz.

Period versus frequency

Long and slow waves, such as ocean surface waves, are often talked about by how long their period is rather than their frequency. Short and fast waves, like audio and radio waves, are usually described by their frequency. Some common ways to change between these two are shown below:

Related quantities

• Rotational frequency, usually shown with the Greek letter ν (nu), measures how quickly something spins around. It tells us how many times an object turns in a given time.
• Angular frequency, shown with the Greek letter ω (omega), is about how fast something moves in a circle. It connects the spinning motion to angles and waves.
• Spatial frequency, shown with ξ (xi), is like counting how often something repeats in space instead of time, such as patterns or waves moving from place to place.

In wave propagation

Further information: Wave propagation

When waves move through materials where their speed does not change with frequency, the frequency is connected to the distance between wave peaks, called the wavelength. For these waves, frequency is found by dividing the wave’s speed by its wavelength.

In empty space, such as a vacuum, the speed of light can be used instead. When waves move from one material to another, their frequency stays the same, but their wavelength and speed can change.

Measurement

See also: Frequency meter

To find out how often something happens, we count how many times it happens in a certain amount of time. For example, if 71 events happen in 15 seconds, we divide 71 by 15 to get about 4.73 events per second, which we call hertz (Hz).

One way to measure frequency is by using a special light called a stroboscope. This light flashes repeatedly, and we adjust its flash rate until the moving object looks still. At that point, the flash rate matches the object's moving speed, and we can read the frequency from the stroboscope.

For higher frequencies, we use a tool called a frequency counter. This electronic device counts how many times a signal repeats in a set time and shows the result in hertz on a digital screen. It can measure many types of vibrations and movements after they are changed into an electronic signal.

For very high frequencies, we use a method called heterodyning. We mix the unknown frequency with a known frequency using a special device, which creates a new signal we can measure with a frequency counter. This lets us measure frequencies much higher than what normal counters can handle.

Examples

Light

Main articles: Light and Electromagnetic radiation

Visible light is a type of wave that travels through space. The frequency of this wave decides its color. Lower frequencies appear red, while higher frequencies look violet. Frequencies below what our eyes can see are called infrared, microwaves, or radio waves. Frequencies above what we see are called ultraviolet, X-rays, or gamma rays. All these waves move at the same speed in empty space.

Sound

Main article: Audio frequency

Sound travels as waves of pressure and movement in air or other materials. The frequency of a sound wave mostly decides how high or low the pitch sounds. Humans can usually hear sounds between 20 Hz and 20,000 Hz, but this range changes with age. Some animals, like dogs, can hear higher frequencies than humans.

Line current

Main article: Utility frequency

In many parts of the world, including Europe, Africa, Australia, and parts of Asia and South America, household electricity alternates at a frequency of 50 Hz. In North America and some other areas, it alternates at 60 Hz. This difference can be noticed as a "hum" in audio recordings from different regions.

Aperiodic frequency

Aperiodic frequency measures how often something happens that isn't repeating in a cycle, like certain random events. It is measured in a special unit called reciprocal second (s⁻¹) or, for things like radioactivity, in a unit called becquerel.

We find this frequency by counting how many events happen in a certain amount of time. This helps us understand how quickly these non-repeating events occur.