Frequency

Jai Ganesh · Today 16:12:09

Frequency

Gist

Frequency is the measure of how often a repeating event occurs per unit of time, typically measured in Hertz (Hz), which means cycles per second, and applies to oscillations, waves (sound, light), and rotations. It tells you how many times a wave passes a point or a vibration completes a cycle in one second, with higher frequencies meaning faster, more frequent events.

Frequency is the number of times a repeating event occurs per unit of time, and its SI unit is the Hertz (Hz), which means one cycle or event per second. It quantifies how often something vibrates, oscillates, or repeats, like sound waves or radio signals, and is the inverse of the period (time for one cycle).

Summary

Frequency, in physics, is the number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion. A body in periodic motion is said to have undergone one cycle or one vibration after passing through a series of events or positions and returning to its original state. See also angular velocity; simple harmonic motion.

If the period, or time interval, required to complete one cycle or vibration is 1/2 second, the frequency is 2 per second; if the period is 1/100 of an hour, the frequency is 100 per hour. In general, the frequency is the reciprocal of the period, or time interval; i.e., frequency = 1/period = 1/(time interval). The frequency with which the Moon revolves around Earth is slightly more than 12 cycles per year. The frequency of the A string of a violin is 440 vibrations or cycles per second.

The symbols most often used for frequency are f and the Greek letters nu (ν) and omega (ω). Nu is used more often when specifying electromagnetic waves, such as light, X-rays, and gamma rays. Omega is usually used to describe the angular frequency—that is, how much an object rotates or revolves in radians per unit time. Usually, frequency is expressed in the hertz unit, named in honour of the 19th-century German physicist Heinrich Rudolf Hertz, one hertz being equal to one cycle per second, abbreviated Hz; one kilohertz (kHz) is 1,000 Hz, and one megahertz (MHz) is 1,000,000 Hz. In spectroscopy another unit of frequency, the wavenumber, the number of waves in a unit of distance, is sometimes used.

Details

Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light.

The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second.

Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or occur repeatedly in geometry or space.

The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz.

Definitions and units

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 ν (the Greek letter nu) is also used. 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

f = 1/T.

The term temporal frequency is used to emphasise that the frequency is characterised by the number of occurrences of a repeating event per unit time.

The SI unit of frequency is the hertz (Hz), named after the German physicist Heinrich Hertz by the International Electrotechnical Commission in 1930. It was adopted by the CGPM (Conférence générale 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. 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. Sixty rpm is equivalent to one hertz.

Stroboscope

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.

Frequency counter

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.

Heterodyne 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 convert higher frequencies, several stages of heterodyning can be used. Current research is extending this method to infrared and light frequencies (optical heterodyne detection).

Additional Information

Frequency refers to the number of complete waves or cycles that occur in a specific unit of time, typically measured in hertz (Hz), where one hertz equals one cycle per second. This concept is central to understanding various wave phenomena, including sound and electromagnetic waves. The period of a wave, which is the length of time it takes for one complete cycle to occur, is the reciprocal of frequency. For instance, a wave frequency of 100 Hz corresponds to a period of 0.01 seconds.

Frequency, wavelength, and speed are interrelated properties of waves. The speed of a wave depends on the medium through which it travels; for example, sound waves travel at different speeds in air and water. Additionally, the Doppler effect explains how the frequency and wavelength of waves change based on the relative motion of the source and the observer. Frequency also plays a vital role in determining the characteristics of waves, such as whether they are in or out of phase, influencing phenomena like constructive and destructive interference. Overall, frequency is a fundamental concept in both physics and various applications, impacting fields ranging from acoustics to telecommunications.

Cyclic Phenomena

The term "cycle" generally indicates something that goes around in a circle. In physics, "cycle" indicates that a specific property or function has a value that progresses through a succession of other values and returns to the starting value in a precise manner that repeats. Phenomena that exhibit this behavior are associated with either circular or sinusoidal wave motions and properties. Such motions can be described by the same math functions, the sine and cosine.

The sine and cosine functions are themselves simple ratios of the lengths of the two sides of a right triangle at one vertex. The radius (plural: radii) of the circle can be rotated about the center by any amount to form the corresponding angle. A vertical line to the point on the circumference where it meets the displaced radius forms a right triangle with a base that is proportionately shorter than the length of the radius. In this right triangle, the displaced radius forms the hypotenuse and the vertical height of the triangle is the opposite. (The "opposite" is the side of the right triangle that is opposite the angle formed at the center of the circle.) The base of the triangle is called the "adjacent." The sine of the angle formed by the base and the hypotenuse is just the ratio of the length of the opposite to that of the hypotenuse (i.e., the radius). Likewise, its cosine is the ratio of the length of the adjacent to that of the hypotenuse. The reciprocal values of the sine and cosine are called the "secant" and "cosecant," respectively.

As the radius rotates, the angle that it forms at the center changes continuously. The value of the sine also changes accordingly. A graph of this variation produces the sideways S-shaped curve that is recognized as a sine wave. The value of the cosine follows the same pattern but is shifted from the sine values. The cosine at any angle has the value of the sine of an angle that is greater by 90 degrees.

There are two methods of describing the amount of rotation about the center, or axis of rotation. In one, the amount is stated in degrees of rotation, with one full revolution totaling 360 degrees. The other measurement of angles is in radians (rad). One radian is the angle formed by two radii when the length of the circumference they mark off is equal to the radius of the circle. There are 2π radians in one complete revolution.

Properties of Cyclic Phenomena

All cyclic phenomena, whether wavelike or circular, share several characteristics. The primary feature of all of them is that their behaviors or values repeat in the same regular way. The number of times that the cycle of any particular phenomenon repeats in a specific amount of time is its frequency. The most common of these is revolutions per minute (rpm) for rotational movements of physical objects, and cycles per second (cps) for wavelike properties. The conventional unit for cps is hertz (Hz), in honor of Heinrich Hertz (1857–94), for his contributions to the physics of electromagnetism (EM). The term is most often used to refer to EM waves.

The duration of just one cycle of the phenomenon is the period of the cycle. The period is calculated simply as the reciprocal value of the frequency. For example, a wave frequency of 100 cps has a corresponding period of 1/100, or 0.01, seconds per cycle (spc). If that same wave is progressing, or propagating, at a speed of 100 meters per second (m/s), each cycle will have moved it through a distance of 1 meter. Since this corresponds to the distance covered by just one complete cycle of the wave, it is the specific wavelength. Wavelength is only used to describe phenomena that travel through space or time. It is not applied to rotational motions.

Frequency, Wavelength, and Speed

EM waves such as visible light all travel at the same speed—the speed of light. Physical waves, such as sound, travel at different speeds determined by the density of the medium. The speed of sound in air, for example, is 331 meters per second (about 1,086 feet per second) at 0 degrees Celsius (32 degrees Fahrenheit), and 342 meters per second (about 1,122 feet per second) at 18 degrees Celsius (65 degrees Fahrenheit). In water, the speed of sound is about 1,140 meters per second (about 3,740 feet per second). The greater the density of the medium is, the more it can transmit sound waves. Another factor that affects the transmission of both physical and EM waves is the relative motion of the wave source and the observer or receiver of the emitted waves. When the two move toward each other, the apparent frequency of the waves increases and the apparent wavelength decreases, but if they move apart, the apparent frequency decreases and the wavelength increases. This is known as the "Doppler effect." It accounts for the apparent changes to the sound of a passing train, as well as the red shift and blue shift in the light observed from distant stars.

For physical waves, speed, frequency, and wavelength are all related. For EM waves, however, the constant speed of light requires that the frequency and wavelength are related in a manner that maintains the constancy of the speed of light.

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Frequency

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