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. The period is the duration of one cycle in a repeating event. So the period is the reciprocal of the frequency.

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 Latin letter f or by a Greek letter ν (nu).

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 . 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): $omega=2pi f,$ . Angular frequency is measured in radians per second (rad/s).

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

T = frac{1}{f}. The SI unit for the period is the second (s).

Measurement

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 T) and then compute the frequency f as the reciprocal of this time:

f = frac{1}{T}.

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

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_0pm Delta f

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.

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 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.

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)

References

External links

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Last updated on Sunday March 09, 2008 at 19:01:25 PDT (GMT -0700)
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