Frequency

=== Counting ===
Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period, then dividing the count by the period. For example, if 71 events occur within 15 seconds the frequency is:
<math display=block>f = \frac{71}{15 \,\text{s}} \approx 4.73 \, \text{Hz}.</math>
If the number of counts is not very large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time.{{cn|date=April 2024}} The latter method introduces a [[random error]] into the count of between zero and one count, so on [[average]] half a count. This is called ''gating error'' and causes an average error in the calculated frequency of <math display="inline">\Delta f = \frac{1}{2T_\text{m}}</math>, or a fractional error of <math display="inline">\frac{\Delta f}{f} = \frac{1}{2 f T_\text{m}}</math> where <math>T_\text{m}</math> is the timing interval and <math>f</math> is the measured frequency. This error decreases with frequency, so it is generally a problem at low frequencies where the number of counts ''N'' is small.

{{multiple image
| align = right
| direction = vertical
| header   = 
| image1   = Resonant reed frequency meter.jpg
| caption1 = 
| image2   = Czestosciomierz-49.9Hz.jpg
| caption2 = 
| width    = 300
| footer   = A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current.  It consists of a strip of metal with reeds of graduated lengths, vibrated by an [[electromagnet]].  When the unknown frequency is applied to the electromagnet, the reed which is [[resonance|resonant]] at that frequency will vibrate with large amplitude, visible next to the scale.
}}