Frequency

Lore & Background

Frequency is a fundamental property of cyclical phenomena such as oscillations, waves, and simple harmonic motion, defined as the number of occurrences of a repeating event per unit of time. The conventional symbol for frequency is *f* or the Greek letter nu (ν). The period *T*, representing the time taken to complete one full cycle, is the reciprocal of frequency, expressed by the relationship *f* = 1/*T*. Temporal frequency specifically emphasizes the count of repetitions per unit time. The SI unit of frequency is the hertz (Hz), named after physicist Heinrich Hertz and adopted by the International Electrotechnical Commission in 1930, later officially replacing the older term "cycle per second" (cps) by the CGPM in 1960. A traditional unit for rotating mechanical devices is the revolution per minute (rpm), where 60 rpm is equivalent to one hertz. Longer, slower waves like ocean surface waves are often described by period rather than frequency, while short, fast waves such as audio and radio signals are typically characterized by frequency. Related quantities include rotational frequency, which measures the rate of change of rotations over time; angular frequency, expressed in radians per second and equal to frequency multiplied by 2π; and spatial frequency, which applies to properties varying over space rather than time. For periodic waves in nondispersive media, frequency is inversely related to wavelength, and when electromagnetic waves travel between media, their frequency remains constant while wavelength and speed change.

Reader's Guide

Frequency is a fundamental parameter across science and engineering, describing how often a repeating event occurs per unit time. Its reciprocal, the period, is used for longer and slower waves like ocean surface waves, while frequency is preferred for short and fast waves such as audio and radio. Related quantities include rotational frequency (rate of change of number of rotations) and angular frequency (rate of change of angular displacement, ω = 2πf). Spatial frequency applies to properties varying in geometry. For periodic waves, frequency relates to wavelength and phase velocity: f = v/λ. Measurement methods include counting events over a time interval, which introduces gating error, and using a stroboscope for rotating or vibrating objects. The hertz, as the SI unit, standardizes frequency measurement globally.

Did You Know?

• Sixty rpm is equivalent to one hertz.
• Angular frequency is frequency multiplied by 2π.
• For electromagnetic waves in vacuum, frequency equals the speed of light divided by wavelength.