Understanding Transverse Waves, Refraction, Frequency, and Its Applications

The assignment content discusses various aspects of frequencies, including the formation of oscillations in magnetic or electric fields, refraction, and the relation between frequency and time. It also touches upon methods for measuring frequencies, such as counting, stroboscope, heterodyne, and frequency counters. Additionally, it highlights the uses of frequency equations in calculating frequencies in various cases like line current, light, sound, and types of frequencies including aperiodic, audio, cut-off, etc. Furthermore, it explains how to calculate frequency in physics through velocity and wavelength.

Blog Writing

Topic: Frequency Equation
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.
Some of the important areas if the use of the frequency equation are explained below:
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.
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.
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
traveled 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 traveled 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 various practical use. Some of the widely used methods of measuring frequencies
include the following:
 Method of counting- this is one of the simplest method 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.

Uses of frequency equations
The frequency equation can be used for calculating frequencies in several cases some of
which are as follows:
 Line Current Case- Frequency is used to measure, alternating current in the household
electrical outlets. In countries like Asia, Australia, Russia, Europe, and South
America,
 Light- Light is a form of electromagnetic wave, which is made of oscillations in
magnetic and electric fields. These frequencies are invisible to the normal human eye.
These frequencies are to be calculated to estimate the speed and frequency of the
waves.
 Sound- The sound waves are the waves which are caused by the mechanical
vibrations. The sound waves occur in substances or air and are waves of pressure and
displacement. In some of the medium, the speed of the sound is independent of the
frequency, and therefore the wavelength of the sound waves is inversely related to the
level of frequency.
Types of frequencies
Some of the various types of frequencies include the following:
 Aperiodic frequency- It is a non-cyclic phenomenon and includes random processes
like radioactive decay. These are generally measured as reciprocal of seconds.
 Audio Frequency- These include the periodic vibrations, which are within the band
which is audible to humans and represented in Hertz. These frequencies are also
affected by environmental factors.
 Cut-off frequency- These are used in electrical engineering and physics. It is also
known as break frequency, or corner frequency. These are the frequencies which are
either below or above the power output of a circuit. These are also represented in
Hertz.
Calculation of frequency in physics
The subject of Physical has some of the vital use for the frequency. To order to calculate the
frequency, the velocity is divided by the wavelength, which is then converted into meters to
determine the level of frequency. The value is then represented in Hertz which is a unit of
frequency. Another use of frequency equation in physics is through the wave equation. It is a
linear partial equation of second-order and are used for light waves or mechanical waves.

Some of the other fields where the frequency equation is highly used include fluid dynamics,
acoustics, and electromagnetics.