Frequency Unit

According to physics,  frequency is generally defined as the number of waves that pass through a fixed point with respect to a unit time. The frequency can also be defined as the number of cycles or vibrations of a body that are undergone in one unit of time with periodic motion.  The periodic motion of the body can be in the form of one cycle or one vibration that passes through a series of events or positions and returns to the original state. Which is similar to the angular velocity or simple harmonic motion. 

This article explains, what is frequency, frequency formula, frequency unit, frequency measurement methods,  types of frequency with examples are given here.  

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How to Calculate Frequency? 

The frequency of the wave can be calculated by taking an account of the time taken by the wave to complete one cycle or one vibration. If the wave takes ½ seconds to complete one cycle or vibration, then the frequency of the wave is 2 seconds.  If the wave takes about 1/100 hours to complete a cycle or vibration, then the frequency of the wave is 100 per hour. 

Usually, the frequency of the wave is inversely proportional to the period of time or time interval. 

Which means, Frequency (f) = 1/time or 1/ time interval. 

On average, the Moon takes slightly more than 12 cycles per year to complete a revolution around the earth.  Likewise, the frequency of a string in a violin is about 440 vibrations or cycles per second. 

Frequency Symbols

The frequency of the wave is generally represented by the word (f). Sometimes, the frequency of the wave can represented by the greek letter nu (𝛎) and omega (ω).  Generally, the greek word nu (𝛎) can be used to determine the frequency of electromagnetic wave-like,  X-rays, UV rays and gamma rays.  The letter Omega (ω) can be used to describe the angular frequency of an object or particle. The angular frequency shows the direction of rotation of the object or the revolution of the object in radians per unit time. 

The German physicist Heinrich Rudolf Hertz found the expression for denoting the frequency in the International Electrotechnical Commission in 1930. The SI unit of frequency is hertz (Hz). So, the frequency unit is generally denoted by Hertz. 

One hertz is equal to one cycle per second. 1000 Hz is equal to one kilohertz (kHz) and  1,000,000 Hz is equal to one megahertz (MHz). In spectroscopy, the frequency of the wave can also be represented in other words such as the wavenumbers, number of waves per unit distance..etc.  Here, the cycles of the waves are usually calculated with the seconds. And the traditional unit for calculating the rotating mechanical devices is with revolution per minute(rpm). One hertz (Hz) is equal to 60 rpm. 

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Types of Frequency 

Angular Frequency 

The rate of change of angular displacement or the rate of change of argument of the sine wave or the rate of change of phase of a sinusoidal waveform is defined as the angular frequency. The angular frequency is usually expressed in terms of omega (ω). 

y(t) = sin(θ(t)) = sin (ωt) = sin (2πft)

dθ/dt= ω = 2πf

The angular frequency is usually measured in terms of radians per second (rad/s). For the discrete-time signal, the angular frequency can be expressed in terms of radians per sampling interval. Because the discrete-time signal is the dimensionless quantity. Usually, the angular frequency is greater than the ordnance frequency by factor 2π. 

Spatial Frequency  

The spatial frequency is similar to the temporal frequency. But the time axis in the temporal frequency is replaced by one or more spatial axes. 

y(t) = sin(θ(t, x)) = sin (ωt + kx)

dθ/dx= k

Here, the wavelength number k represents the spatial frequency and is measured in radians per metre. If the wave has more than one spatial dimension, then the wavenumbers are vector quantities. 

If the periodic waves are in non dispersive media, then the frequency will have an inverse relationship with the wavelength λ. In the dispersive media, the frequency f of the sinusoidal wave is directly proportional to the phase velocity v and inversely proportional to the wavelength of the wave λ.  

It can be represented as 

f = v/ λ

For the electromagnetic waves moving in the vacuum, the velocity is replaced by the speed of light. So, v = c. Then the frequency can be calculated by f = c /  λ

If the monochromatic light propagates from one medium to another, then the wavelength and speed of the wave will change and the frequency will remain the same. 

What is Cumulative Frequency? 

The sum of a total number of frequencies that lies below or above the reference value is known as the cumulative frequency. 

What is Frequency Distribution? 

The frequency distribution shows the graphical or tabular representation of the frequency observed by observers for a particular time. The frequency distribution is of three types, ungrouped frequency distribution, grouped or cumulative frequency distribution and relative frequency distribution. 

What is Frequency Polygon? 

The pictorial representation by graphical means of frequency distribution is known as the frequency polygon. This method helps to analyse the shapes of the distribution. 

What is Frequency Modulation? 

Frequency modulation is one of the most commonly used modulation methods in the communication system. If the frequency of the carrier waves is modulated according to the frequency of the message wave, then the modulation technique is known as frequency modulation. Usually, they prefer such techniques as the frequency of the message wave cannot transfer long distances without any loss. 

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Instruments Used to Measure Frequencies 

• In the olden days, people used Stroboscopes to measure the frequency of rotating or vibrating objects.  

• People used an electrical device called a frequency counter to calculate the high-frequency waves.  The frequency counter shows the result in Hertz. 

• The frequency of the waves, which lies above the level of a frequency counter, can be measured through the Heterodyne method. 

This article explained the frequency formula, frequency symbols, types of frequency, frequency polygon, frequency modulation,  instruments that are used to measure the frequency of waves in detail.