Frequency Equation

Frequency Equation: Explanation and Types

Some of the important areas if the use of the frequency equation are explained below:

Frequency is calculated using the number of times an incidence took place in per unit of time. There can be angular frequency, temporal frequency, and spatial frequency. The period is used as the reciprocal of frequency and it represents per cycle. It is one of the important metrics used in engineering and science to calculate the rate of vibrations, oscillations, radio signals, audio signals, etc. Now our experts from Assignment Help UK will tell you about important areas of use.

  • Vibrations– It is a type of mechanical phenomenon in which the oscillations take place in an equilibrium point. These oscillations can be random or periodic depending upon the situation. Further, the vibrations can also be classified as desirable or undesirable. Thus the frequency equations can be used, for designing which can reduce the undesirable vibrations. Some of the examples of desirable vibrations include playing of a loudspeaker, sound from a mobile phone, operation of woodwind instrument. Some of the examples of undesirable vibrations include vibrations in electric motors or engines, or from a various mechanical device. These vibrations are generally caused through the various imbalance in rotational parts of the instrument. Some of these are even caused by gear teeth or friction in the parts. There are several studies in engineering and science which identify the relationship between vibrations and sound.
  • Oscillations– It is a type of phenomenon, which is caused through repetitive vibrations which have occurred in time or between different states. These mechanical oscillations are identified and calculated through vibrations and frequency equation. Some of the real-world examples of oscillations include alternating current, a pendulum swinging. This occurrence of the oscillations can also take place in dynamic systems, and some of the important areas of medical science. Like the human heart, beating is calculated through the oscillations in frequency equations. It also has some use in economics, to calculate the business cycles of boom and recession. It is used in geology, to calculate the vibrations in geothermal geysers. It is also used to calculate the nerve cell periodic firings. In the area of astronomy, it is used to know the Cepheid stars.
Frequency Equation
Frequency Equation

Units used in the frequency equation

The unit of frequency which is most commonly used is Hertz. This unit has been called after the physicist, Heinrich Hertz. The denomination one hertz, indicate the event is repeated once in each second. Thus if an instrument has a 1-hertz rate of a refresh, it means that the instrument will change the picture once in each second. This unit was previously known as cycles in each second. Also in the traditional times, revolutions per minute were used as a measurement for rotating of mechanical devices.

The unit of the frequency describes the number of waves that passes a place in a given amount of time. The abbreviated form of the unit of frequency in Hz. Now our experts from Assignment Writing Service will tell you important types of frequency equation.

Important types of frequency equation

Angular Frequency– This frequency is represented by omega, and indicates the rate of change of waveform phase or rate of displacement of angular, etc. It is generally measured, using radians per second. This frequency is also larger than the regular frequency. 

Spatial Frequency– It is also known as temporal frequency, and used to calculate wavelength. It is measured in radians per minute, as the wavelength is a vector quantity.

Frequency equation

Frequency equation indicates the wavelength, velocity and period. With a given value of the velocity and wavelength, the frequency can be calculated. Before calculations, the wavelength is converted into meters. And finally, the velocity is divided by the wavelength. Thus in simple terms, the formula can be represented as:

Frequency= Velocity/Wavelength

Various types of waves used in frequency equation

There are several types of waves which exists in a real-life situation. Some of these include:

  • Longitudinal Wave– It is one of the sound waves in which the displacement is in the same direction, to the direction of the propagating wave. These are also known as compressional waves, as they create compressions while moving through a medium and also cause changes in the pressure. These include the seismic waves and the sound waves. The waves formed in the medium can be round or straight.
  • Transverse Wave– This is also an important wave used in frequency equations. In this type of wave, the displacement in the medium is at the ninety degrees to the propagation direction. These waves are generally mechanical in the sense that it requires an elastic medium for transmission. These are also known as shear waves and abbreviated as T-Waves. The example of such wave will the oscillations which are generated through the drum. One of the most commonly used transverse waves is light in which the oscillations are formed around the magnetic or the electric field. The motions of these waves can be represented through the mathematic formulas.
  • Refraction– These waves are the waves which change its direction when it travels from one medium to another. These also include the change in the speed with the alteration of the wavelength. Another form of refraction is diffraction, in which the waves bend due to obstacles or openings. The level of diffraction increase with the increase in the size of the wavelength. An example of such a wave is the coastline of an ocean or sea. When the waves reach the shores, it gets distorted or refracted, which changes the velocity and the direction. Another example of refraction is the bending of the light waves when it passes from one substance to another. Similarly, the sound wave also bends when it passes from one substance to another.

The relation between frequency and time

The concept of frequency and time are related but are distinct from one another. The concept of frequency indicates how often, something takes place and the period indicate the time which is taken. Thus frequency can be represented as a rate quantity, and period is represented as the time quantity. Frequency is denominated in cycles/second and period is denominated as seconds per cycle. One of the example which will help understand this difference is as follows:

Let’s consider a woodchopper who drums at a periodic rate to cut the tree. Let’s assume that the woodchopper drums at the rate of two times per second, the frequency can be said as 2 Hertz. As each of the drums will be enduring for one-half of a second, the period can be indicated as 0.5s. 

If the situation changes and the woodchopper drums the tree 4 times in one second, then the frequency will be calculated as 4Hertz. And at the same time, the drums have to endure the drum for a period of one-fourth of a second. Therefore the period can be written as 0.25s. This example helps to explain the relationship which can be represented mathematically as,

Period = 1/frequency and frequency= 1/period

The relation between frequency and speed

The concept of frequency is also sometimes confused with the concept of speed. The concept of speed indicates how fast the object is moving and is represented in terms of distance travelled per period. In the case of a wave, speed will be the distance completed by a point in a wave in any given period. Thus there is a difference between the wave speed and wave frequency. The wave frequency is the number of cycles which occur in each second. And the idea of wave speed indicates the distance in meters travelled in each second. The characteristic of the wave is that it can travel back and forth but with lesser speed. Similarly, the wave can travel back and forth but with higher speed. Thus they two represent distinctly different quantities.

Measurement of frequencies in a frequency equation

The frequency equation used in maths and science helps in the calculation of the frequencies which has a various practical use. Some of the widely used methods of measuring frequencies include the following:

  • Method of counting– this is one of the simplest methods to know the frequency of a repeating event. It can be done by simply counting the number of times, that the event took place in a specified period. This value is then divided by length of the period to indicate the frequency. In a situation when the number of counts is not large, it is better to measure the time interval for the number of occurrences which is pre-determined. Another method is to calculate the number of occurrence within a specific time. But the latter measure has higher chances for creating the random error. This is also known as gating error in scientific terms and creates an average error in the calculation of the frequency. This error decreases with the frequency, and therefore this problem is faced at low frequencies.
  • Stroboscope Method– Another method used for measurement of frequencies is called stroboscope. It is a traditional method in which the vibrations or the rotations of an object is calculated. It is similar to the intense flashing light which is occurring repetitively, and whose frequency can be adjusted with the help of the calibrated circuit of time. In this mechanism, the strobe light is pointed towards the rotating object and the level of frequency is adjusted up or down. In the situation when the frequency of the rotating object equals the frequency of the strobe, the object finishes one cycle of oscillations. The level of frequency is read from the calibrated readout which is present on the stroboscope. One of the biggest disadvantages of this method is that an object rotating at an integral multiple of the strobing frequency with tend to appear stationary.
  • Heterodyne method– This method is generally used in electromagnetic signals, in which the frequencies are measured through heterodyning. In this process, a non-linear mixing device is used, to mix unknown frequency with the known frequency. This non-linear device is called a diode. This leads to the generation of the beat signal and creates heterodyne between two frequencies. When these two signals are close, the level of heterodyne generated is very low and therefore cannot be measured with the help of a frequency counter. Thus this method can only be used to measure the difference between the reference frequency and unknown frequency. To reach a higher level of frequencies, various stages of heterodyning is used. There are several research which is being conducted to use this method in case of light and infrared frequencies.
  • Frequency Counter– This method is generally used to measure higher frequencies. It is a type of electronic instrument, which helps in measurement of the frequency of a repetitive electronic signal. It has a digital display system which displays the outcome in hertz. It uses the method of digital logic, to measure the number of cycles, during a period, based on quartz time. This method can also be used for some of the cyclic processes, that may not be electrical. These include the rate of rotation of a shaft, calculation of sound waves, and calculation of mechanical vibrations, which are converted into electronic signals with the help of transducers. In the most recent inventions of 2018, the frequency counters can be used to include a range of about 100 GHz. This acts as one of the limitations of the direct counting method, and therefore any frequency above this is measured through an indirect method. For more information related to this topic or other topics, you can also check with Do My Assignment UK.