Frequency

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For other uses, see Frequency (disambiguation).
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.

Frequency is a measure of the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.

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[edit] Definition and units

For cyclical processes, such as rotation, oscillations, or waves, frequency 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 Latin letter f or by a Greek letter ν (nu).

In SI units, 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.

The period is usually denoted as T, and is the reciprocal of the frequency f:

T = \frac{1}{f}.

The SI unit for period is the second (s).

[edit] Measurement

[edit] By timing

To calculate the frequency of an 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.

In experimental work (for example, calculating the frequency of an oscillating pendulum) it is more accurate to measure the time taken for a fixed number of occurrences, rather than the number of occurrences within a fixed time. The latter method introduces — if N is the number of counted occurrences — a random error between zero and one count, so on average half a count, causing an biased underestimation of f by ½ f / (N + ½) in its expected value. In the first method, which is more accurate, frequency is still calculated by dividing the number of occurrences by the time interval; however it is the number of occurrences that 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 T) and then compute the frequency f as the reciprocal of this time:

f = \frac{1}{T}.

A more accurate measurement can be obtained by taking many cycles into account and averaging the periods 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 f=f_0\pm \Delta f.

[edit] Frequency of waves

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

f = \frac{v}{\lambda}.

In the special case of electromagnetic waves moving through a vacuum, then v = c0 , where c0 is the speed of light in a vacuum, and this expression becomes:

f = \frac{c_0}{\lambda}.

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

[edit] Examples

[edit] Period versus frequency

As a matter of convenience, longer and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are usually described by their frequency instead of period. These commonly used conversions are listed below:

Frequency 1 mHz (10-3) 1 Hz (100) 1 kHz (103) 1 MHz (106) 1 GHz (109) 1 THz (1012)
Period (time) 1 ks (103) 1 s (100) 1 ms (10-3) 1 µs (10-6) 1 ns (10-9) 1 ps (10-12)

[edit] Other types of frequency

  • Angular frequency ω 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):
\omega=2\pi f\,.
Angular frequency is measured in radians per second (rad/s).
  • Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
  • Wavenumber is the spatial analogue of angular frequency. In case of more than one space dimension, wavenumber is a vector quantity.

[edit] See also

Electronics Portal

[edit] References

  1. ^ Accidentally, 1 hertz is the approximate frequency of a human heart (Herz in German language)

[edit] External links

Look up frequency, often in Wiktionary, the free dictionary.