Frequency definition and the frequency formula

Frequency (lat. Frequentia, notation for ν) is a physical quantity that produces the number of repetitions of a periodic phenomenon in a unit of time (periodic motion). It is equal to the inverse of the duration of one of the recurring events, period T, that is:

f = \frac{1}{T}

The unit of frequency is hertz (Hz), which is a unique name for the reciprocal second (HZ = 1 / s)

Angular frequency of circular frequency or pulsation is the product of frequency and number 2 pi.

\omega = 2 * \pi * f

Periodic motion is the motion of a body that returns to the same position after equal time intervals (period of motion). It is often in nature and technique; for example, all types of pendulums, planer tools in machining materials, planets around the Sun, and the like move periodically. Factors or parameters of periodic motion are the same as for oscillations.

Frequency unit

Angular frequency units are radians per second (rpm) or reciprocal seconds (1 / s) equal to hertz.

Frequency describes periodic phenomena, such as motion along closed curves, motion around an equilibrium position, changes in the quantity value around an equilibrium value (oscillation), propagation of changes in some properties or states (waves), and others. In undulating phenomena, the relationship between frequency and velocity v propagation is constant:

f * \lambda = v

, where is the lambda wavelength, the distance between the nearest points of a state of oscillation.


To determine the frequency of events, the number of events we observe in a given time interval we divide by the duration. In the International System of Units (SI), we measure the result in units of hertz (Hz), named after the German physicist Heinrich Rudolf Hertz. 1 Hz represents the repetition of events once per second, 2 Hz twice per second, and so on. This unit was initially called cycle per second (cps), which is still used today. Other measurements of frequency are revolutions per minute (rpm) and radians per second (rpm). Heart rate and musical tempo we measure it in beats per minute (BPM).

An alternative method of determining the freq is to measure the time between two consecutive repetitions of an event (period) from which we calculate the frequency as the reciprocal value of that time:

f = \frac {1}{t}

where: t – time. Even more accurate measurement involves counting multiple cycles and determining the average duration of the period.

How to use the frequency calculator?

Our calculator uses the above formulas to calculate the frequency.

Wave frequency

Measuring the frequency of sound, electromagnetic waves (such as radio waves or light), electrical signals, etc. The frequency in hertz is the number of repeating waveform cycles per second. If it is a sound wave, it is the frequency that largely characterizes the pitch. Frequency has an inverse relationship to the term wavelength. The frequency f is equal to the velocity v of the wave divided by the wavelength λ (lambda) of the wave:

f = \frac{v}{\lambda}

In the special case when an electromagnetic wave travels through a vacuum, then v = c, where c is the speed of light in a vacuum, so the expression becomes:

f = \frac{c}{\lambda}

Note: Also when waves pass from one medium to another, their frequency does not change – only their wavelength and speed change.


Except in the modification by the Doppler effect, the frequency is a constant quantity in space. It cannot change by any physical process that includes effects related to propagation speed or wavelength.

The Doppler effect or Doppler effect is a change in the frequency of waves with the relative motion of their source or observer. We observe it with each wave motion as an increase or decrease when the wave source and the observer approach or move away from each other.

Examples and How to calculate frequency from the period?

The frequency of a standard tone A above the middle C is usually defined as 440 Hz, i.e., 440 periods per second, known as a concert tone, to which the orchestra tunes.

Children can hear freq up to approximately 20 kHz, but these freq become less and less audible as people grow older.

In Europe, the AC frequency is generally 50 Hz (close to tone G). However, in North America, the AC frequency is 60 Hz (close to elevated tone B, slightly less than a third above the freq in Europe). The interference frequency in the sound recording can show where the recording was made – in Europe or in America.

Input the time in which one wave cycle occurs (period). The calculator will determine the freq.

Also, you can use this calculator to determine the period if you know its freq.

How to calculate the freq from wavelength?

Enter the wave velocity into the second field or choose the type of wave and its medium from the list in the first field. By default, it is set to light in a vacuum.

Enter the wavelength, and the frequency value will appear.

Frequently Asked Questions

What is frequency?

In physics, frequency is the number of waves that pass through a given point in one unit of time; it is also the number of cycles or vibrations that a body in periodic motion undergoes in one unit of time.

How to find wavelength from frequency?

The following formula can be used to compute wavelength: wavelength = wave velocity/frequency. Wavelength is often stated in meters.

What is the relationship between frequency and wavelength?

The relationship between frequency and wavelength is inverse. The wavelength of the wave with the most significant frequency is the shortest. One-half the wavelength is equal to twice the frequency. As a result, the wavelength to frequency ratio is the inverse of the frequency to wavelength ratio.

What is frequency measured in?

The SI unit for frequency is the hertz (Hz). One hertz is the same as one cycle per second.

What is the unit of fq?

Frequency is defined as the number of periods or cycles per second. The hertz is the SI unit of frequency (Hz). One hertz equals one cycle every second.

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