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For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term frequency is defined as the number of cycles or repetitions per unit of time. The conventional symbol for frequency is f or tag_hash_109 (the Greek letter nu) is also used.[3] The period T is the time taken to complete one cycle of an oscillation or rotation. The frequency and the period are related by the equation[4] f = 1 T . {\displaystyle f={\frac {1}{T}}.}

The SI unit of frequency is the hertz (Hz),[4] named after the German physicist Heinrich Hertz by the International Electrotechnical Commission in 1930. It was adopted by the CGPM (Confrence gnrale des poids et mesures) in 1960, officially replacing the previous name, cycle per second (cps). The SI unit for the period, as for all measurements of time, is the second.[5] A traditional unit of frequency used with rotating mechanical devices, where it is termed rotational frequency, is revolution per minute, abbreviated r/min or rpm.[6] 60 rpm is equivalent to one hertz.[7]

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As a matter of convenience, longer and slower waves, such as ocean surface waves, are more typically described by wave period rather than frequency.[8] Short and fast waves, like audio and radio, are usually described by their frequency. Some commonly used conversions are listed below:

For periodic waves in nondispersive media (that is, media in which the wave speed is independent of frequency), frequency has an inverse relationship to the wavelength, tag_hash_114 (lambda). Even in dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength tag_hash_117 of the wave: f = v . {\displaystyle f={\frac {v}{\lambda }}.}

An old method of measuring the frequency of rotating or vibrating objects is to use a stroboscope. This is an intense repetitively flashing light (strobe light) whose frequency can be adjusted with a calibrated timing circuit. The strobe light is pointed at the rotating object and the frequency adjusted up and down. When the frequency of the strobe equals the frequency of the rotating or vibrating object, the object completes one cycle of oscillation and returns to its original position between the flashes of light, so when illuminated by the strobe the object appears stationary. Then the frequency can be read from the calibrated readout on the stroboscope. A downside of this method is that an object rotating at an integer multiple of the strobing frequency will also appear stationary.

Higher frequencies are usually measured with a frequency counter. This is an electronic instrument which measures the frequency of an applied repetitive electronic signal and displays the result in hertz on a digital display. It uses digital logic to count the number of cycles during a time interval established by a precision quartz time base. Cyclic processes that are not electrical, such as the rotation rate of a shaft, mechanical vibrations, or sound waves, can be converted to a repetitive electronic signal by transducers and the signal applied to a frequency counter. As of 2018, frequency counters can cover the range up to about 100 GHz. This represents the limit of direct counting methods; frequencies above this must be measured by indirect methods.

Above the range of frequency counters, frequencies of electromagnetic signals are often measured indirectly utilizing heterodyning (frequency conversion). A reference signal of a known frequency near the unknown frequency is mixed with the unknown frequency in a nonlinear mixing device such as a diode. This creates a heterodyne or "beat" signal at the difference between the two frequencies. If the two signals are close together in frequency the heterodyne is low enough to be measured by a frequency counter. This process only measures the difference between the unknown frequency and the reference frequency. To reach higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection).

All of these waves, from the lowest-frequency radio waves to the highest-frequency gamma rays, are fundamentally the same, and they are all called electromagnetic radiation. They all travel through vacuum at the same speed (the speed of light), giving them wavelengths inversely proportional to their frequencies. c = f , {\displaystyle \displaystyle c=f\lambda ,} where c is the speed of light (c in vacuum or less in other media), f is the frequency and tag_hash_121 is the wavelength.

Sound propagates as mechanical vibration waves of pressure and displacement, in air or other substances.[11] In general, frequency components of a sound determine its "color", its timbre. When speaking about the frequency (in singular) of a sound, it means the property that most determines its pitch.[12]

The frequencies an ear can hear are limited to a specific range of frequencies. The audible frequency range for humans is typically given as being between about 20 Hz and 20,000 Hz (20 kHz), though the high frequency limit usually reduces with age. Other species have different hearing ranges. For example, some dog breeds can perceive vibrations up to 60,000 Hz.[13]

In many media, such as air, the speed of sound is approximately independent of frequency, so the wavelength of the sound waves (distance between repetitions) is approximately inversely proportional to frequency.

In order for these new clocks to be used for national and global timekeeping, scientists need to be able to compare signals from clocks across distances. Optical frequency combs can help achieve that too. NIST and JILA, a joint research institute of NIST and CU Boulder, used lidar to send time signals through the air, comparing two different kinds of atomic clocks.

Advanced optical atomic clocks also allow scientists to study the constants of nature beyond our own planet. For example, with the help of optical frequency combs, NIST scientists are using these improved clocks to search for elusive dark matter.

Optical frequency combs also are helping scientists search for exoplanets around distant stars. By tracking the exact colors of light from these stars, they can look for a wobble in the motion of a star that would indicate the presence of an Earth-like planet orbiting the star.

Optical frequency combs work over long distances. In 2013, NIST patented lidar, a light detecting and ranging system that utilizes optical frequency combs to measure the distance to an object by analyzing light reflected from it.

Atoms and molecules can be identified by which frequencies of light they absorb. Since optical frequency combs generate millions of frequencies in short pulses, they can be used to quickly and efficiently study the quantity, structure and dynamics of various molecules and atoms.

This has many potential applications and is already being used to study pollution. Using optical frequency combs, scientists at JILA have studied short-lived molecules that link burning fossil fuels to air pollution. The structure and dynamics of large and complex molecules can also be probed by frequency combs.

Scientists are also working on using optical frequency combs to detect trace amounts of various molecules in gases. In 2019, scientists and engineers from NIST, University of Colorado Boulder, and LongPath Technologies developed a dual-comb, portable spectroscopy system to detect minute methane emissions from oil and gas fields.

The optical frequency comb may have applications in medicine as well. Just as it can be used in chemistry applications, the comb could be used to detect trace molecular indicators of disease. Scientists at JILA have been experimenting with combs to create breathalyzers that detect disease.

Optical frequency combs emit a continuous train of very brief, closely spaced pulses of light containing a million different colors, spanning from the invisible infrared through the visible and into the ultraviolet spectrum.

Physicists had been toying with the idea of this specialized laser since the 1970s, when Theodor Hnsch of the Max Planck Institute for Quantum Optics in Germany proposed a model for the first optical frequency comb while he was at Stanford University. Scientists knew that continuous lasers could only produce one color of light, but pulsed lasers could generate multiple colors. The shorter the pulse, the more frequencies the laser could produce.

Hall and his team of physicists at JILA, including Steven Cundiff, Scott Diddams, David Jones and Jun Ye, developed several other techniques that pushed the optical frequency comb closer to reality. In the late 1990s, the team developed a calibration system for the femtosecond laser, creating controllable, well-defined pulses containing thousands of colors. They had also improved stabilization for the laser, making it steady. In 2005, Hall and Hnsch shared part of the Nobel Prize in Physics for their contributions to the optical frequency comb.

While many frequency combs currently are about the size of a shoebox and are widely available for use in and outside of laboratories, scientists have been working diligently to shrink them. Scientists have been working to produce optical frequency combs so small they can fit on a microchip.

Many scientists hope that if frequency combs can fit on a microchip, they can have even greater commercial applications. Microcombs have the potential to improve communications systems, particularly within data centers and other high performance computing systems. The spectroscopy power of optical frequency comb could be incorporated into smartphones and wearable technology to monitor health.

Research is making progress to overcome those hurdles. Even if a complete comb-on-a-chip is never realized, microcombs are already finding uses in research. With miniature dual frequency combs, NIST has already developed a chip-scale atomic clock. Scientists at NIST and their collaborators will continue to explore the vast potential for microcombs, fiber laser frequency combs and optical frequency combs. 17dc91bb1f