Frequency

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Frequency is a measure of the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.

[edit] Definition and units

For cyclical processes, such as rotation, oscillations, or waves, it is defined as a number of cycles, or periods, per unit time. In physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a roman letter f or by a greek letter ν (nu).

The number of wavelengths per second of a particular radiation.

In SI system, the unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz. For example, 1 Hz means that an event repeats once per second, 2 Hz is twice per second, and so on ^[1]. This unit was originally called a cycle per second (cps), which is still sometimes used. Heart rate and musical tempo are measured in beats per minute (BPM). Frequency of rotation is often expressed as a number of revolutions per minute (rpm). BPM and rpm values must be divided by 60 to obtain the corresponding value in Hz: thus, 60 BPM translates into 1 Hz.

A related measure of frequency, called angular frequency ω, is often introduced. It is defined as the rate of change in the orientation angle (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves): <math>\omega=2\pi f</math>. Angular frequency is measured in radians per second (s^-1).

[edit] Measurement

[edit] By counting

To calculate the frequency of the event, the number of occurrences of the event within a fixed time interval are counted, and then divided by the length of the time interval.

To calculate the frequency of an event in experimental work however (for example, calculating the frequency of an oscillating pendulum) it is crucial that the time taken for a fixed number of occurrences is recorded, rather than the number of occurrences within a fixed time. This is because your random error is significantly increased performing the experiment the other way around. It [the frequency] is still calculated by dividing the number of occurrences by the time interval, however, the number of occurrences is fixed, not the time interval.

An alternative method to calculate frequency is to measure the time between two consecutive occurrences of the event (the period) and then compute the frequency f as the reciprocal of this time:

<math>

f = \frac{1}{T} </math> where

T= time

A more accurate measurement takes many cycles into account and averages the period between each.

[edit] By stroboscope effect, or frequency beats

In case when the frequency is so high that counting is difficult or impossible with the available means, another method is used, based on a source (such as a laser, a tuning fork, or a waveform generator) of a known reference frequency f₀, that must be tunable or very close to the measured frequency f. Both the observed frequency and the reference frequency are simultaneously produced, and frequency beats are observed at a much lower frequency Δf, which can be measured by counting. This is sometimes referred to as a stroboscope effect. The unknown frequency is then found from <math>f=f_0\pm \Delta f</math>.

[edit] Frequency of waves

Frequency has an inverse relationship to the concept of wavelength,simply,frequency is inversely proportional to wavelength λ. The frequency f is equal to the speed v of the wave divided by the wavelength λ (lambda) of the wave:

<math>

f = \frac{v}{\lambda}. </math>

In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes:

<math>

f = \frac{c}{\lambda}. </math>

When waves travel from one medium to another, their frequency remains exactly the same — only their wavelength and speed change.

Apart from being modified by the Doppler effect or any other nonlinear process, frequency is an invariant quantity in the universe. That is, it cannot be changed by any linearly physical process unlike velocity of propagation or wavelength.

[edit] Frequency of sound

Sound is a wave associated with the transmission of mechanical energy through a supporting medium. It can be shown experimentally that sound cannot travel through a vacuum. The energy available in a sound wave disturbs the medium in a periodic manner. Periodicity is important if a sound wave is to carry information. In air, the disturbance propagates as the successive compression and decompression (the latter sometimes called rarefaction) of small regions in the medium. If we generate a pure note and place a detector (our ear, for example) at a point in the surrounding medium, a distance from the source, the number of compression-decompression sequences arriving at the detector during a unit time interval is called the frequency. The time interval between successive maximal compressions is called the period. The product of the frequency and the wavelength is the velocity.

[edit] Examples

• In music and acoustics, the frequency of the standard pitch A above middle C on a piano is usually defined as 440 Hz, that is, 440 cycles per second (Listen (help·info)) and known as concert pitch, to which an orchestra tunes.
• A baby can hear tones with oscillations up to approximately 20,000 Hz, but these frequencies become more difficult to hear as people age.
• In Europe, Africa, Australia, Southern South America, most of Asia, and in Russia, the frequency of the alternating current in household electrical outlets is 50 Hz (close to the tone G), however, in North America and Northern South America, the frequency of the alternating current is 60 Hz (between the tones B♭ and B — that is, a minor third above the European frequency). The frequency of the 'hum' in an audio recording can show where the recording was made — in countries utilizing the European, or the American grid frequency.

[edit] See also

• Negative frequency
• Angular frequency
• Frequency converter
• Frequency range or frequency band
• Letter frequencies
• Pitch (music)
• Natural frequency
• Wavelength

[edit] Notes

Incidentally, 1 hertz is the approximate frequency of a human heart (Herz in German)

[edit] External links

• Conversion: frequency to wavelength and back
• Conversion: period, cycle duration, periodic time to frequency
• Keyboard frequencies = naming of notes - The English and American system versus the German system
• Teaching resource for 14-16yrs on sound including frequency
• A simple tutorial on how to build a frequency meter
• Frequency - diracdelta.co.uk - javascript calculation.af:Frekwensie

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