Frequency

From Encyclopedia Jr, free information reference for Kids

For other uses, see Frequency (disambiguation).

Sine waves of various frequencies; the lower waves have higher frequencies than those above.

Frequency is the measurement of the number of times that a repeated event occurs per unit of time. It is also defined as the rate of change of phase of a sinusoidal waveform.

[edit] Measurement

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.

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 (see random error). It [the frequency] is still calcualted by dividing the number of occurrences by the time interval, its just that the number of occurrences is fixed, not the time interval.

In SI units, the result is measured in hertz (Hz), named after the German physicist Heinrich Rudolf Hertz. 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 used sometimes. Other units that are used to measure frequency include revolutions per minute (rpm) and radians per second (rad/s). Heart rate and musical tempo are measured in beats per minute (BPM).

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:

where

T is the period.

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

[edit] Frequency of waves

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

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:

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] Examples

• 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, the frequency of the alternating current in mains is 50 Hz (close to the tone G), however, in North America, the frequency of the alternating current is 60 Hz (close to the tone B flat — 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 Europe or in America.

[edit] See also

• Negative frequency
• Angular frequency
• Frequency converter
• Letter frequencies
• Pitch (music)

[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