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How To Find Frequency Of A Wave:7 Quick Facts

January 20, 2024January 31, 2022 by Keerthana Srikumar

frequency is an essential concept in understanding waves and their characteristics. It helps us analyze and interpret various wave phenomena in fields such as physics, engineering, and signal processing. In this blog post, we will explore how to find the frequency of a wave, using different methods and tools. We’ll cover everything from the basic concepts of frequency to practical examples and calculations. So, let’s dive into the fascinating world of wave frequency!

How to Find the Frequency of a Wave

Image by L31n42 – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

A. The Concept of Frequency in Waves

Before we delve into the calculations, let’s establish a clear understanding of what frequency represents in the context of waves. frequency refers to the number of complete cycles or oscillations that a wave undergoes in a given unit of time. It is measured in hertz (Hz), where 1 Hz corresponds to one cycle per second. The higher the frequency, the more oscillations occur in a given time frame.

B. Importance of Frequency in Wave Analysis

frequency plays a crucial role in wave analysis as it provides valuable information about the characteristics of a wave. It helps us determine the pitch of a sound wave, the color of light, the vibration of a guitar string, and even the transmission of radio signals. By understanding the frequency of a wave, we can analyze its behavior, identify patterns, and make predictions about its interactions with other waves or objects.

Calculating the Frequency of a Wave using Wavelength

A. The Relationship between Frequency and Wavelength

To calculate the frequency of a wave using its wavelength, we need to understand the relationship between these two parameters. wavelength refers to the distance between two consecutive points in a wave that are in the same phase, such as two peaks or troughs. It is usually denoted by the Greek letter lambda (λ).

The relationship between frequency (f), wavelength (λ), and wave velocity (v) is given by the wave equation:

$v = f cdot lambda$

In simpler terms, the wave velocity is equal to the product of frequency and wavelength. By rearranging the equation, we can solve for frequency:

$f = frac{v}{lambda}$

B. Step-by-step Guide to Calculate Frequency using Wavelength

Here’s a step-by-step guide to calculating the frequency of a wave using its wavelength:

Determine the wavelength (λ) of the wave. This can be measured directly or obtained from a given problem.
Find the wave velocity (v) of the medium through which the wave is propagating. For example, in the case of sound waves, the wave velocity is the speed of sound in air.
Use the wave equation, (v = f cdot lambda), and rearrange it to solve for frequency: (f = frac{v}{lambda}).
Substitute the values of wave velocity and wavelength into the equation to find the frequency.

C. Worked-out Example on Finding Frequency using Wavelength

Let’s work through an example to illustrate how to find the frequency of a wave using its wavelength. Suppose we have a wave traveling through a medium with a velocity of 343 meters per second (m/s). The wavelength of the wave is measured to be 0.5 meters (m).

Using the formula (f = frac{v}{lambda}), we can calculate the frequency as follows:

$f = frac{343 , text{m/s}}{0.5 , text{m}} = 686 , text{Hz}$

Therefore, the frequency of the wave is 686 Hz.

Determining the Frequency of a Wave using Period

A. Understanding the Concept of Period in Waves

period is another important parameter that can be used to calculate the frequency of a wave. It refers to the time it takes for one complete cycle or oscillation of a wave to occur. The period is denoted by the symbol T and is measured in seconds (s).

B. The Relationship between Frequency and Period

The relationship between frequency (f) and period (T) is the reciprocal of each other. It can be expressed by the equation:

$f = frac{1}{T}$

In other words, the frequency is equal to the inverse of the period.

C. Step-by-step Guide to Calculate Frequency using Period

To calculate the frequency of a wave using its period, follow these steps:

Determine the period (T) of the wave. This can be measured directly or obtained from a given problem.
Use the equation (f = frac{1}{T}) to calculate the frequency.
Substitute the value of the period into the equation to find the frequency.

D. Worked-out Example on Finding Frequency using Period

Let’s work through an example to demonstrate how to find the frequency of a wave using its period. Suppose we have a wave with a period of 0.01 seconds (s). Using the equation (f = frac{1}{T}), we can calculate the frequency as follows:

$f = frac{1}{0.01 , text{s}} = 100 , text{Hz}$

Therefore, the frequency of the wave is 100 Hz.

How to Find the Frequency of a Wave in Python

Image by Frequency-modulation.png – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

Python is a powerful programming language that can be used for various scientific and mathematical calculations, including wave analysis. By utilizing Python’s libraries and functions, we can easily calculate the frequency of a wave. One such library commonly used for wave analysis is NumPy.

B. Python Code to Calculate Wave Frequency

Below is an example of Python code that calculates the frequency of a wave using the wavelength:

“`python
import numpy as np

def calculate_frequency(wavelength, wave_velocity):
frequency = wave_velocity / wavelength
return frequency

wavelength = 0.5
wave_velocity = 343

frequency = calculate_frequency(wavelength, wave_velocity)
print(“The frequency of the wave is:”, frequency, “Hz”)
“`

C. Worked-out Example on Finding Frequency using Python

Let’s use the Python code above to find the frequency of a wave with a wavelength of 0.5 meters (m) and a wave velocity of 343 meters per second (m/s).

The output of the code will be:

The frequency of the wave is: 686.0 Hz

Therefore, the frequency of the wave, calculated using Python, is 686 Hz.

How to Find the Frequency of a Wave in MATLAB

MATLAB is a widely-used programming language and environment for numerical computations and data analysis. It offers powerful tools and functions for wave analysis, making it convenient to calculate the frequency of a wave. MATLAB’s built-in functions, such as fft and ifft, are particularly useful for frequency analysis.

B. MATLAB Code to Calculate Wave Frequency

Here’s an example of MATLAB code that calculates the frequency of a wave using the wavelength:

“`matlab
wavelength = 0.5;
wave_velocity = 343;

frequency = wave_velocity / wavelength;
disp(

$'The frequency of the wave is:', num2str(frequency), ' Hz'$

);
“`

C. Worked-out Example on Finding Frequency using MATLAB

Let’s use the MATLAB code above to find the frequency of a wave with a wavelength of 0.5 meters (m) and a wave velocity of 343 meters per second (m/s).

The output in MATLAB will be:

The frequency of the wave is: 686 Hz

Therefore, the frequency of the wave, calculated using MATLAB, is 686 Hz.

Special Cases in Finding the Frequency of a Wave

A. How to Find the Frequency of a Sine Wave

When dealing with a simple sine wave, finding its frequency becomes relatively straightforward. The frequency of a sine wave is determined by the number of complete cycles it completes in a given time frame. You can calculate the frequency by measuring the time it takes for one complete cycle and taking the reciprocal of that duration.

B. How to Find the Frequency of a Sound Wave

In the case of sound waves, determining their frequency is crucial for understanding their pitch and musical notes. Sound waves are mechanical waves that propagate through a medium, such as air or water. To find the frequency of a sound wave, we can use various methods, including Fourier analysis, tuning forks, or digital audio processing techniques.

C. How to Find the Frequency of a Standing Wave

Standing waves occur when two waves of the same frequency and amplitude traveling in opposite directions interfere with each other. Finding the frequency of a standing wave involves analyzing the nodes and antinodes of the wave pattern. By measuring the distance between adjacent nodes or antinodes and the wave velocity, we can calculate the frequency of the standing wave.

How does the frequency of a wave impact the properties of diffraction in waves?

The frequency of a wave plays a crucial role in determining the properties of diffraction. Diffraction refers to the bending and spreading of waves as they pass through an opening or encounter an obstacle. The Properties of Diffraction in Waves article provides a comprehensive understanding of how various factors, including frequency, influence this phenomenon. Higher frequencies typically result in smaller diffraction angles, while lower frequencies lead to larger angles. This relationship highlights the intricate connection between the frequency of a wave and its diffraction behavior.

Common Misconceptions and Errors in Finding the Frequency of a Wave

how to find the frequency of a wave — Image by Konung yaropolk – Wikimedia Commons, Wikimedia Commons, Licensed under CC0.

A. Does the Frequency of a Wave Change?

The frequency of a wave remains constant throughout its propagation, regardless of any changes in amplitude or wavelength. While the wave’s characteristics may vary, such as its speed or shape, the frequency stays the same. It is an inherent property of the wave that determines its pitch, color, or any other audible or visible attribute.

B. Finding the Frequency of a Wave without the Speed

To find the frequency of a wave, we need to know either the wavelength or the wave velocity. Without one of these parameters, it is not possible to calculate the frequency directly. However, in some cases, we can infer the frequency indirectly by analyzing the wave’s behavior, interference patterns, or using other mathematical techniques such as Fourier analysis.

Understanding how to find the frequency of a wave is essential for analyzing and interpreting wave phenomena in various fields. Whether you are studying waves in physics, analyzing sound signals, or processing digital data, the ability to calculate the frequency provides valuable insights. By utilizing the relationships between frequency, wavelength, period, and wave velocity, we can uncover the hidden treasures hidden within the fascinating realm of waves. So go ahead, explore, and discover the wonders of wave frequency!

Also Read:

3 Destructive Interference of Wave example: Detailed Facts

January 21, 2024January 31, 2022 by Keerthana Srikumar

Destructive interference of wave example is a more straightforward way to understand the concept in the easier way possible.

When we take certain actual life events into consideration, we end up learning the concept in an easy way. Destructive interference of wave examples has a direct influence on the learning process of such concepts.

Gravitational Wave
Radio Wave
Automobile Muffler
Speaker Waves
Musical Instruments

Gravitational Wave

Gravitational waves have two different kinds, and they are gravitational solid weak gravitational waves.

Here in this condition, only the weak gravitational force will be considered to interact with each other waves. When two waves mix or go hand in hand with each other, then there will be a specific process occurring.

The process mainly depends on how the two waves interfere with each other. If the amplitude of the wave seems to be the same then, the resultant wave is said to be a destructive interfered wave.

When the crest of one wave meets the top node that is the crest of another wave, we get a resultant wave. This happens when the waves meet up with each other in the exact location. When the end wave is larger than the individual wave, we call it destructive interference.

There is also another question saying, what if the higher wave meets the weaker wave? They generally act like the water wave in mechanical terms. When we know that two waves are interfering with one another, there will definitely be a result in terms of destruction.

The weaker wave of gravitational force is basically like one of the light and the sound waves. In this wave, there is energy present as in there will also be mass in the wave, so when one strong wave pulls another weak wave, there are chances for a black hole scenario.

The wave of gravitational is that they will travel at different speeds and different locations. So finding the frame is a little tricky. Hence this is how the destructive interference comes into action.

When two different waves travel, and when they interfere with each other due to the amplitude values, they will cancel out each other. This is the reason behind the destructive interference occurring with waves in contact with one another.

Radio Wave

The radio wave is one of the electromagnetic waves that have a lower frequency. The radio wave will come under the destructive interference of wave example. There will be destructive interference happening within.

Radio waves are generally used for transmission and primarily for sound waves. In specific devices, radio waves are being used since they are the lightest wave and can be received quickly. Radars are setups that used mainly use radio waves in order to transmit and receive signals.

When the signals have been transmitted in terms of waves, there are chances for them to interfere with one another. When such a thing happens, the waves merge and are large or merge and be small, depending upon the amplitude of the individual waves.

The radio waves have the wavelength that is available in the electromagnetic spectrum. These waves are used in radios because the waves are helpful in transmitting and receiving signals in an easy way that the waves can be detected instantly.

While the waves are being transmitted, they will undoubtedly interfere with each other. When the waves interfere with the crest of the wave and the trough of another wave, then there is said to be destructive interference.

The resultant wave is more significant if only the interference is constructive, but if the wave is minimal compared to the individual wave, then they are said to be destructive interference. So radio waves will come under destructive interference of wave example.

destructive interference of wave example — **“Classic old radio 1960s or 70s style” by theslowlane is licensed under CC BY 2.0**

Automobile Muffler

The automobile muffler is attached to any vehicle because they are termed as the noise canceller in vehicles.

The mufflers are run by the concept of destructive interference. The waves travelling in the same medium and in the exact location will cancel out on each other because of the different amplitudes.

The muffler is nothing but a silencer called in the local term. What happens in the muffler is that the gases let out by the vehicle will be internally combusted using the internal combustion mechanism.

The air-bone noise in the vehicle is usually reduced by the combustion method, and the muffler is used to lessen the process. The waves present in the process will cancel out each other.

The cancellation of the waves is mainly due to the ends of opposite sides meeting one another. The crest of one wave, that is, the top node of the wave, meets the trough of another wave that is the bottom node of the wave.

So the crest and trough of two waves meeting one another will eventually cancel out each other. The resultant wave will be a wave with a smaller amplitude. The muffler is basically one of the sound destructive interference of wave examples.

Speaker Waves

Say there are two speakers kept in a vast hall, so when the music is turned on, if the sounds coming from the speakers do not match, then we call it as destructive interference of wave example. The speakers mainly deal with the sound waves in general.

The waves in the speaker travel as sound, and when they cancel out on each other, it is termed destructive interference. The amplifier also contributes in some way to cancel out the wave. The sound is amplified, and when it reaches the speaker, so the sound waves play a significant role in delivering the music to the listeners.

The destructive interference is the one where the waves having different phase differences will negate each other. Therefore we get a wave as a result where the amplitude is much smaller than the individual one.

The speaker must be connected to the amplifiers for a better result as it will deliver a much better sound of music. So the destructive interference of waves will be there in speakers that deliver different sounds with different frequencies.

4 6 — **“Creative Speakers” by DeclanTM is licensed under CC BY 2.0**

Musical Instruments

The guitar comes under the category of musical instruments, which has mainly sound waves connected with each other.

Mainly flute deals with the sound waves by itself without the aid of the secondary instrument. So all kinds of musical instruments come under destructive interference of wave examples. The waves often tend to interfere with each other in the process of transmitting the sound signal to the surroundings.

5 2 — **“People’s musical instruments, Ukraine” by be creator is licensed under CC BY 2.0**

In guitars, the waves travel in such a way that they often interfere and be destructive or constructive. So tuning in guitars is essential so that when they are heard through the speaker, the sounds are in phase with each other.

The destructive interference is due to the negation of two waves when they encounter each other in the same medium and at the exact location. Hence in such cases, it is normal to have waves being interfered with.

Also Read:

5 Constructive Interference Examples: Detailed Facts

January 21, 2024January 29, 2022 by Keerthana Srikumar

Constructive interference example in the real world will allow us to understand what happens in the micro-level of physics.

When two waves having the same amplitudes interfere with each other, they will have the resultant wave displace in the same medium with the equivalent amplitude as the original ones. Let us see a few constructive interference example and understand the process of the interference.

Interference of Colors
Single Slit Diffraction
Young’s Double Slit Experiment
Water Pool
Speakers
Musical Instruments

Interference of Colors

Interference in itself is one of the constructive interference example. Let us see how this works. Firstly what is interference? It is the co-joint of two waves that into contact with each other.

Waves can exist in all forms, namely light, sound and electromagnetic. Waves are made up of two different factors known as the crest and trough; here, the crest means the top node of the wave and the trough is the down node of the wave.

These top and down nodes of a wave make a big difference when two of such waves go hand in hand with each other. Say when these waves meet, they interfere, meaning internally, they are in phase with one another.

When the top nodes of one wave meet another, that is, the crests of two waves meeting one another are termed as constructive interference. Now let us see how this concept works well in terms of colors when considered.

Bubble colors are said to be one of the constructive interference examples. There are different colors that come under constructive interference. Namely yellow and magenta, where their crests meet another crest and form a wave pattern.

Let me also tell you that diffraction is the after effect of the interference phenomena. Where the colors generally are deflected at various different angles so finally form a final image. They interfere with each other, so we get a new pattern of waves, sometimes different colors too.

1 6 — **“Colouring Pencils” by Golden_Ribbon is licensed under**

Single Slit Diffraction

Well, one can ask what single slit diffraction has to do with constructive interference example. Actually, it does, if not in the process the definitely in the end product.

The single slit experiment is to show how light waves bend around the corner of any target surface and how well it forms a resultant wave pattern in the same medium or rather a different one.

When we allow the light to enter a slit of the dimension that corresponds to the wavelength of the light been allowed to pass through, now when a ray of light passes through the slit, the light undergoes diffraction and appears as a new type of wavelet.

Now how does this become a constructive interference example? The resultant wave will depict whether the wave has been constructive or destructive in nature. The angle at which the light has been displaced in a new position will actually tell about the type of interference.

The wave after hitting the target will be allowed to propagate in a specific direction so that the wavefront is formed accordingly. The waves coming out of the slit will interfere with each other in no time.

If the wave increases in a particular way, then we need to know that it is a constructive interference so that we get to see a beam of light in the process.

**“File:Hex1quantum22.GIF” by Ferman is licensed under CC BY-SA 2.0**

Young’s Double Slit Experiment

The experiment is more or less connected to the single-slit experiment. There it was just a single slit, but in this experiment, we see double openings for the light waves to propagate.

The experiment also deals with bringing out the true nature of light, whether it is a particle or a wave. Indeed it seems to be a wave since it gives a beam in the end result.

So it can also be under the category of constructive interference examples where the resultant wave adds up with each other creating large waves altogether. Their amplitude is the same since the top and down nodes meet each other.

Depending upon the type of wave pattern is made when the light wave hits the slits, we decide whether the interference is constructive or destructive. So the angle at which the light wave hits the slit makes a significant impact on the resultant pattern of the wave.

The angle at which the light wave hit the target is supposedly taken into account. The reason is when it comes out as a wavefront in which the angle and the number of waves present will decide the type of interference.

**“File:2slits.png” by self is licensed under CC BY-SA 3.0**

Water Pool

The water pool is one of the best ways to understand the interference pattern, and also it is an easy constructive interference example. So this is considered as an experiment in some instances to understand the interference concept better.

For example, consider a person standing inside the pool and striking both hands back and forth. So it will definitely make wave patterns. So when the hands go front and back, the troughs, as in the waves, will cancel out inside.

The cancelling is termed to be destructive interference. And when the waves keep on adding up each other, then it is constructive interference. The reason is, as mentioned earlier, the nodes of both top and bottom will meet each other, and it will result in the wave pattern having amplitude with a more significant value.

The interference made by the wave will have a circular pattern, and they are regarded to be the wavefront, meaning, and the secondary wavelets that comes from the primary waves that mix with each other.

Here we see the constructive interference since the wave in the water pool is added with each other when the water is stroked by hand back and forth. The crest and crest of two waves basically meet at their nod points.

4 4 — **“Swimming Pool Pattern #4” by Lee Edwin Coursey is licensed under CC BY-SA 3.0**

Speakers

Speakers are an excellent constructive interference example as they will ensure the sound waves have been heard by the listener when put out loud in a vast hall.

Basically, when there are two speakers kept in a hall and when they both are played together, then they are said to have a constructive interference pattern. The process goes like this, beginning the sound coming from both the speakers must be of the same amplitude.

The reason for the amplitude to be the same is that only then the sound is heard in the same measure. The crests of both the waves must be in such a way that they are equal and meet each other at the exact location.

When we consider the sound waves to have the same amplitude, then the waves have their respective nodes in a point where the tops and bottoms meet at the same point and are in phase. The frequency of the sound is also the same when it is connected to on single source, so there is not much loss of energy in such cases.

There are also possibilities for destructive interference when the waves do meet but end up cancelling out each other. That is when the crest of one wave is the bottom part of a wave meets the crest that is the top part of a wave, meeting one another at the same point.

Hence when the sound comes out of both, the speakers appear to be the same simply because they have the same amplitude and even when the wavelength and such factors affect the sound waves.

5 1 — **“speaker :-)” by Tim Geers is licensed under CC BY 2.0**

Musical Instruments

Musical instruments are a great way to explain the constructive interference example. They have sound waves that interfere with each other and give a result in the form of constructive or destructive.

Mainly string instruments contribute mainly to constructive interference. Let’s take guitar as an example for this concept. When we tune guitars in such a way that while it is played, we can hear a neat, pleasant tune and the reason is that constructive interference has occurred in the process of tuning.

The reason why mostly the strings instruments are being tuned is that when they are playing, we need to hear the sound, which is in phase and is cordial. The sound waves that resulting out of the played instrument arrange themselves in a pattern where there is no disturbance in the way it has been delivered.

The wave’s presence increases as it is played because they add up each other, and the amplitude is in such a way that it is more significant than the individual amplitude of the wave. So the crests of the wave’s present will undoubtedly team up at one point and the same, also the troughs too.

In this way, we can hear a piece of better music, and less amount of noise will be coming out of the instruments. And this is the main reason why the string instruments are always tuned before they are played.

Let us see how there are side effects present in such cases. There is something called the beat frequency. Sound is made up of several waves together, which has different frequencies, and when the entire wave meet each other, they either add up or cancel out. So we formally find a constructive interference pattern here.

Also Read:

3 Destructive Interference of Light Example: Detailed Facts

January 21, 2024January 29, 2022 by Keerthana Srikumar

Destructive interference of light example is a way to understand how the interference pattern works.

Various destructive interference of light example is there, but we take into consideration the primary factors and ways that help us understand the concept better. Here are a few of those, and let us look into detail.

Light beams
Moving Electrons
Slit Experiments
Interferometer

Light beams

The light beam comes under the category for so many examples. So the light beams nothing but a collection of several numbers of light waves in one single bundle.

The term light beam means the direction of light from a source that acts in one particular direction when emitted. It differs from source to source. The target surface plays a significant role in determining the type of interference the light beams undergo when they hit on a surface.

Let us take an example of several experiments that will explain better about the light beams in one of the destructive interference of light example. When we consider an incident light to fall on a surface, it will either be reflected or refract or sometimes diffract too.

All these conditions of light will mainly depend on the type of the target surface. When the surface is said to be smooth or glass instead, the light will reflect back into the same medium but at a different angle than that of the incident angle.

Also, when the target surface seems to be rough, the light beam will refract and also, if there are curves in the target object, there will be diffraction. So all that we understand from these events is that light beams, when considered a wave, will interfere with each other.

Once they interfere, it will be either constructive or destructive depending upon the angles or the type of wave that is being interfered with. For in sound waves, the interference will occur and show destructive interference if any two waves cancel out on each other.

If the two light waves are said to be located at 180⁰ that are also in two different phases, it eventually will negate each other resulting in amplitude having a smaller value than the individual waves.

destructive interference of light example — **“Light Beam” by romainguy is licensed under**

Moving Electrons

We clearly need to understand the moving electron concept since there are several ways in which the electron movement has been determined and sued for many other experiments.

How do we bring the moving electrons under destructive interference of light example? Here it is we use simple experiments to show that the moving electron will reveal a destructive interference.

Electron, as we all know, is a particle that is one single entity and thus does not produce any secondary wave patterns all by itself; instead, with the aid of specific equipment, it will be on the whole be terms as a function of the wave.

Now consider a source that produces a series of electrons which, when allowed through a small gap or pinhole, will produce further series of single electrons. So what actually happens when the electrons are allowed through the hole?

See, when the light in the form of the particle is allowed through an outlet that is pretty small, it will pass through it at a particular angle. So based on the incident angle, the outcome will be studied. The result is influenced by the incident angle, too, based on which the wave pattern is decided.

The light particle in the form of the electron will pass through the hole and come out on the other side as several particles at a different location based on the angle. When we connect the entire lying here and there in points, we will get a wave pattern.

The wave pattern obtained after connecting the electron points after the transmission will form a conclusion if they have been constructive or destructive in terms of interference. When the wave pattern obtained is negated due to the trough and crest meeting of the two sets of the wave function is then termed as destructive interference.

2 8 — **“The city through a slit” by Wajahat Mahmood is licensed under CC BY-SA 2.0**

Slit Experiments

Experiments like this will showcase the true nature of light, whether it is a particle or a wave, and if it is a wave, what are the possibilities for it to interfere and form a pattern.

Let us consider the single slit experiment, which has only a single slit gap. Here we allow the light wave to pass through the single whole and see the secondary wavefront appearing on the other end of the slit.

So when these light waves enter a hole and leave, they will form a particular wave pattern depending on certain factors that aid it. Say when the wave patterns appear to more and increasing order, then it is said to be a constructive pattern.

The waves forming a pattern will indeed undergo an interference process, and if it does, so there are two chances, either constructive or destructive. When bot the nodes of the wave, namely crest and trough, meet each other respectively at the exact location, then it is termed as constructive interference.

But when the crest of one wave and then the trough of another wave go hand in hand with each other, it is said to be destructive interference. The destructive interference depends on the measure of amplitude too.

When the amplitude of both the waves is said to be indifferent values, they will indeed cancel out on each other since they have different phase differences within. So the resultant wave will have amplitude that is undoubtedly smaller compared to the resultant wave of constructive interference.

3 6 — **“File:Single slit and double slit2.jpg” by Jordgette is licensed under CC BY 4.0**

Interferometer

The interferometer is one of the best destructive interference of light example as it will not only tell us about the interference pattern but also the type of interference.

Basically, what happens in an interferometer is that one single beam of light is split into two beams and is allowed to propagate into two different paths. So by this way, the two waves will interfere with one another and give a result based on the meeting of the waves.

4 5 — **“Atom interferometer” by europeanspaceagency is licensed under CC BY-SA 3.0**

When the divided light beams are allowed to propagate, they will produce fringes, and this will form a wave pattern in order. When the waves formed cancel out each other instantly, then this will come under destructive interference of light example.

In this experiment, there will be a microscope that will focus on the resultant wave and let us know about the type of interference. When the two nodes of a wave do not match with one another, then it is termed destructive interference.

The interferometer will generally merge the two incoming waves from different sources or by dividing a light beam into two. From this very process, the destructive interference pattern can be observed in order.

Also Read:

Constructive Interference vs Destructive Interference: Detailed Facts

January 21, 2024January 28, 2022 by Keerthana Srikumar

Constructive interference vs destructive interference is a more superficial comparison to understand the wave interaction.

CONSTRUCTIVE INTERFERENCE	DESTRUCTIVE INTERFERENCE
Two waves sum up each other	Two waves negate each other
Crest and crest meet one another	Crest and trough meet one another
The resultant wave has a larger amplitude	The resultant wave has a smaller amplitude

Now we shall see what factors aid in determining the difference between constructive interference and destructive interference.

Constructive interference vs destructive interference considering Amplitude
Constructive interference vs destructive interference considering Wave’s
Constructive interference vs destructive interference considering Frequency

We must take note of the type of wave we must consider before they interfere with one another. Basically, when two waves interfere with each other, that process is termed to be interference.

When one wave interferes with another wave and results in a larger wavelength, it is termed constructive interference, and when two waves interfere with each other, resulting in a smaller wavelength, then it is termed destructive interference.

Generally, when in constructive interference, the two waves meeting each other with the same amplitude will result in the wave having an amplitude that is larger than the individual wave. This is mainly seen in speakers playing the same music, and we hear the same music but very much louder.

In destructive interference, the two waves which go hand in hand with each other will always have a resultant displaced wave having amplitude that is small. The crest of one wave meeting the trough of another cordially gives way for destructive interference.

We can see the destructive interference example in daily life. The destructive interference concept is applied in the technology level, that is, headphones being a noise canceler. The amplitude will be much smaller compared to that of constructive interference.

Constructive interference vs destructive interference considering Amplitude

The constructive interference is termed as such because the two waves meeting one another will have their respective amplitudes. When they encounter each other, the amplitudes of the two waves will merge and result in one single wave of equal amplitude.

The wave appearing in the same medium being a resultant has an amplitude that is way much higher. So, in this case, the medium in which the constructive interference occurs will have an upward displacement.

The resultant upward displacement of the resultant wave is larger than the individual displacement of the two waves interfering. The constructive interference occurs along with medium and in the same direction as the originating waves.

Let us take an example where the constructive interference is influenced by the amplitude. Consider two pulse waves travelling in the same medium also in the same direction. They will have particular amplitude individually.

In destructive interference, the waves having a 180⁰ phase will cancel out each other if the two are positive and negative. The individual amplitude value is larger than the final wave of amplitude that is way much smaller.

The waves interfering have nodes which are called the ends of the wave. The constructive and destructive have the nodes that match at the exact location, which is the resultant wave of the interference process.

Constructive interference vs destructive interference considering Wave’s

Wave patterns that appear in general are due to the consequence of interference of the two waves colliding with each other.

When the waves interfere, the resultant wave pattern appears in the same direction since the amplitude has the more significant measure. Here the crest and crest meet each other. But in destructive interference, the wave pattern appears opposite to each other.

The resultant wave pattern in a destructive interference will always have an opposite where the crest of one wave will meet the rough of the other wave. Also, the amplitude of the displaced wave will be smaller than the individual waves that interfere with each other.

Let us see how wave patterns are formed when the interference process takes place in a pool. When we stand inside the pool with both hands stretched and move back and forth, there will arise a wave pattern.

The wave pattern is simply the wavefronts of the primary waves when they undergo interference. When both hands have been stroked back and forth, it will form a wave pattern. The troughs in the wave pattern will cancel out each other.

The cancelling of the troughs of the wave is termed destructive interference. The area of the wave pattern which keeps on increasing is a sign of the addition of the waves. This is termed constructive interference.

These wave patterns are essential not only in water sound but mainly in light too. In light, when the light waves hit a surface that has a gap in it, the diffraction pattern is obtained. When one single beam enters the hole, it will come out as a whole set of waves.

2 7 — **“Constructive Interference” by Clearly Ambiguous is licensed under**

Constructive interference vs destructive interference considering Frequency

Generally, constructive interference occurs when the crest and crest of two interfering waves meet each other. Due to this, the amplitudes also will add up and form a wave pattern of the same individual waves.

When the Frequency of the waves appear to be the same, then the resultant wave will be the same and appear in the same medium. When we consider the sound waves, the sound will be heard more in constructive interference.

When a number of cycles happen at a particular point given is certainly termed to be the frequency and it also related to amplitude of the resultant.

Hence when constructive interference vs destructive interference occurs, it will have so many factors that will influence the secondary wave pattern in general.

4 3 — **“Wave interference, South Island, NZ” by brewbooks is licensed under**

Frequently Asked Questions

What is the interference of light?

When the two light waves interfere with each other is termed light interference.

The disturbance of light due to one deformed wave will lead to the interaction of the two waves. Interference of light occurs if the light waves have the same amplitude, Frequency and also should be coherent.

What is the destructive interference example?

Noise-cancelling headphones are one of the prominent examples of destructive interference.

When the headphone has a microphone attachment, it will gradually pick up the Frequency of the waves of the incoming. So the amplitude will be less when the resultant wave is displaced in opposite to one another.

What is a good interference example?

One good example of sound wave interference is musical instruments.

For instance, let us consider guitar. When two guitars are tuned in phase, they will sound the same when played. But if the tuning is different, we get to hear different notes while hearing. When speakers play a sound, if they play with the same amplitude, then we call it constructive interference.

Also Read:

Reflection vs Diffraction: Comparative Analysis

January 21, 2024January 27, 2022 by Keerthana Srikumar

$Reflection vs Diffraction: Comparative Analysis 26$

Reflection vs diffraction is one of the standard search terms. Reflection deals with the light wave and Diffraction deals with light and sound.

REFLECTION	DIFFRACTION
The bouncing of light is termed as a reflection	The bending of light in the corner is termed Diffraction
Reflection is concerned with the incident light bouncing back into the same medium	Diffraction is concerned with sound and light traveling from one medium to another
In reflection, light can be a particle or a wave	In Diffraction, the light has to be a wave

On the basis of the comparison we shall discuss the three of the few factors that helps to different reflection and diffraction:

Reflection vs Diffraction in terms of velocity
Reflection vs Diffraction in terms of medium
Reflection vs Diffraction in terms of incident light

The one main difference between reflection vs Diffraction is that one deals majorly with light and the other with sound, although having light in it. Say when a light beam or a ray passes through a medium, the properties will be affected.

In reflection, the incident light hitting the target will either bounce back to the same medium or enter another medium depending upon the type of the medium.

But in Diffraction, the light beam will pass through the medium in and out and will also accompany sound with the passage. Here the factors like frequency amplitude will remain the same when sound is considered.

One main difference is, in reflection, the incident light can act as both particle and wave, but in Diffraction, the incident light must be a wave.

Reflection vs Diffraction in terms of velocity

In reflection, the velocity of the incident light particle or wave is constant because the speed remains unchanged. But the direction component is changed due to the different angles at which the light has been incident on.

Diffraction has specific quantities which will remain unchanged, but speed is sometimes altered accordingly, which appears to be but, in reality, does not. The incident light is hitting at a different angle on the target, so the end result is also at a different angle.

Since velocity is regarded as the vector quantity, it holds both the magnitude and the direction components, where speed is considered to be the magnitude component of it.

Hence both in reflection and in Diffraction, the speed remains unchanged, but the direction changes at different angles each. The reason is that the speed is constant throughout the process irrespective of the source of the incident light and the target being considered.

When velocity is concerned, both reflection and Diffraction will face no change with speed but with direction.

Reflection vs Diffraction in terms of medium

Reflection of incident light mainly depends on the property of the target. If the target surface is smooth and glassy, the incident light will instantly bounce back into the same medium.

Diffraction does not depend on the medium directly but is connected with the refraction, where the light bends around the corner of the target object. In this case, it comes out as a sound too.

When light enters from a rarer medium to a denser medium, there will be a slight change in the speed of light along with a significant change in direction. The reason is that the denser medium will have a different refractive index than the rarer medium.

When the rarer medium is regarded to be air and the denser medium is water or oil, the light passing from another will face a change in the direction and a change in the speed too.

For example, when a ray of light is incident on a mirror, it will reflect back the exact image of the light in return. This is because the light is reflected back into the medium but at a different angle to that of the incident angle.

But in Diffraction, the light ray will enter another medium will, refract, and will bend around the corner of the medium. For example, if we yell inside a room, the wall will stop the reflection, but the sound will stay within the walls.

Reflection vs Diffraction in terms of incident light

For reflection, the incident light can be a wave or a particle, but for Diffraction, the incident light must be a wave.

When a particle of light is incident on a target surface, it will reflect back into the same medium depending upon the type of target surface, but in Diffraction, the incident ray must be a wave in order to bend around corners.

Like we said earlier, when a particle or a wave strikes on a target surface which is a mirror, it will reflect back the exact same image if the particle or a wave in turn. But in Diffraction, if a wave passes through a pinhole, it will refract in the medium and will come out as different sets of light waves.

So for the light to bend around corners and to pass through a pinhole or any type of medium, the incident light must be a wave in order to produce more waves.

3 3 — **“File:Diffraction-red laser-diffraction grating PNr°0126.jpg” by D-Kuru is licensed under**

Frequently Asked Questions

What is refraction?

When an incident light passes from one medium to another, it will change the direction and speed.

If any light wave or a particle moves from a different medium, it will face a change in direction and in speed. Depending upon which the refracted ray will either travel towards the normal or away from the normal. The speed and direction in refraction will vary compared to that of the incident light.

What are refracted rays and diffracted rays?

Refracted ray travels towards or away from the medium, and diffracted ray is the result of the bending of light.

In refraction, the incident light can be a particle or a wave and, depending upon the medium, will move away or towards the normal. But a diffracted ray is the one that is passed through a medium, say a pinhole; coming out of it will be another set of a new wave pattern. A diffracted ray has also sound accompanied with it.

Does a sound wave reflect or refract?

A sound wave can be both reflected and refracted. The reflection and the refraction of sound occur according to the type of medium.

A sound wave in a vast hall is certainly reflected because the medium is large, and there is no other second medium for it to enter. So it is reflected back to back, and that’s how a sound is heard in a place. Also, sound waves require a medium to travel without which it cannot be reflected or refracted. When the medium is not very dense, the sound waves refract, and it will not stop at the boundary of the medium.

Also Read:

What Is Reflection Velocity: How, Why, When, Detailed facts

January 21, 2024January 27, 2022 by Keerthana Srikumar

What is reflection velocity? The reflection velocity is the one that is present when the light passes from one medium to another.

The reflection velocity is usually described as the light which passes with a particular velocity which is regarded as the magnitude component. This value shall remain the same and does not change under any circumstances.

The wave theory of light explains better the question, what is reflection velocity? It says that light is composed of a set of beams that interfere with one another. There is also another assumption that light is a particle and travels with a particular velocity.

All this discussion can be proved and disapproved with a set of experiments in labs. In order to prove this set of hypotheses, we must conduct experiments from which a conclusion can be drawn.

The conclusions drawn give a better platform to discuss the various other factors in the traveling of light. The light travels with a velocity that will remain constant always but could be disturbed under extreme conditions.

When a ray of light travels and hits a surface, it either will reflect or refract. Let us consider the light to be reflected. What is reflection velocity, then? The velocity will remain unchanged under this condition even when the direction is altered.

In the coming sections of topics regarding what reflection velocity is, we shall see in detail how, why, when, and what reflection velocity is.

what is reflection velocity — **Reflection of light**

What happens to velocity during reflection?

In a reflecting medium, the velocity will undoubtedly remain the same. The reason behind this process is that the speed of light changes its path in the course of time.

The speed is altered due to the change in direction if the process is said to be refracted. The term reflection is regarded as when a light particle or a wave, when considered hits a surface and travels back.

In this case, the velocity will actually not change its value, and sometimes depending on the source of light, the speed is altered and will lead to refraction. In all ways, possible velocity will be the same in the medium.

Let us uses an example to understand what is reflecting velocity better. Say a pulse of light travels through a vacuum and strikes on a surface. Depending upon the surface, the light pulse will travel back in the same medium but with a change in direction.

The light pulse encounters a change in direction, although the speed aid for the same. When it changes the direction, eventually, there must be acceleration which is possible due to the change in speed. But the value of speed goes unaltered and light pulse travels back in the same medium with only the change in direction.

Why is reflection velocity important?

Reflection velocity is important because it will explain specific properties of optics which is helpful for any kind of light-related experiment.

Basic phenomena where the light ray hits a smooth surface, it will work for a sure bounce back into the same medium with only a change in direction and not speed. Velocity is a vector quantity. It has components, magnitude, and direction.

The magnitude is referred to as speed, and the direction is referred to be the same. So when a source of light with its respective speed hits a smooth or glass surface, it instantly will bounce back into the same medium as the original.

When the light ray or beam strikes a medium or, say, travels from one medium to another, the value of speed and direction will depend on the type of medium it has been traveled to and from.

Say, for example, when the light beam travels from a rare medium that is air to a denser medium like water or oil, the speed is said to be altered along with the change in direction too. There is a reason for such change occurring in the medium.

We call the reason to be refractive index, and the refractive index will determine how dense the medium is and how much it will alter the speed and the direction of light that has been entered into it.

Hence keeping in mind the case of changes in the speed of light, the type of medium and the properties could easily be determined, and this is helpful for several experiments related to light.

Does reflection change the speed?

Certainly, the reflection of a light beam does not change the speed at all. The main reason being is speed is a magnitude component of velocity since velocity is a vector quantity, and it is composed of both magnitude and direction.

When the light beam, if referred to be reflected, the speed will not change, but only the phase will be altered in that case. But in refraction, it is totally different when the speed is considered.

Say if we consider a light pulse passing from a rarer medium to denser medium depending upon the medium the type of medium. It may be air, water, or oil and anything for that case. So if it travels from air to water, the reflection is absent; instead, the refraction process occurs.

If the surface is considered to be glass, the light ray will bounce back into the same with the same angle also. So here, the speed is not altered, but the direction changed. There are so many other circumstances where the speed of light is said to be changed, but actually, it does not.

So from these instances, we draw a conclusion saying the speed is certainly not changed, but only the direction is changed, and the angle is also determined.

Does reflection change the velocity?

Before we know what this means, let’s get the difference between speed and velocity. Speed is the scalar quantity. It has only magnitude, but velocity is the vector quantity that has both magnitude and direction components.

So when we say speed, it is the magnitude component of the velocity. If the light passes or strikes on a medium, depending upon the type of the medium, the speed and velocity will vary accordingly.

Speed does not change in reflection but the direction will, meaning that velocity will change in the medium if reflection occurs. The light reflecting in the same medium will change the velocity. That is, the direction will change, but the speed here is a constant by all means.

Yes, the reflection will change the velocity of the light in terms of direction but not in magnitude. Although it appears to change the speed in the end, it is the direction that will be altered.

How does reflection change the velocity?

Say when a light ray passes from one medium to another, the reflection occurs in a different form, and we call it refraction.

When the light enters another medium from its origin, the speed is altered; that is, it will increase or decrease depending upon the type of medium and the value of the refractive index. So this will decide whether the velocity change or not in any medium a light ray enters.

For instance, when light is considered to be a wave, it will have a beam that interferes with each other. So when the beam touches the surface, if it is smooth, the light will reflect back into the same medium with the same angle but with a different phase.

The process goes like this, if the ray of light is refracted, the beam of light entering the medium will change the direction, either towards or away from the normal. This will also cause the speed to change over the course of time.

But in reflection, there is no such thing called a change in velocity; velocity wholly means the magnitude and the direction. In reflection, only the direction is changed with the same speed; when viewed closer, there seems to be a change in speed, but in reality, it does not.

Why does reflection change the velocity?

We must understand why reflection changes the velocity. There is also the fact that speed on a velocity does not change, but the direction does.

Keeping the fact that direction is changed in a reflection but not the speed, we come to a conclusion that reflection does change the velocity. Here the direction component changes and the magnitude do not change in any situation.

The reason is that incident light rays have different angles at which they will either reflect or refract. This change in direction is sometimes regarded to the term refraction also. So when it hits a target, depending upon the target, it will reflect at a different angle.

Considering all the cases mentioned above, we now come to a conclusion that the direction component of velocity is changed in reflecting keeping the speed a constant, which is the magnitude.

Reflection of the light beam occurs at different angles since the incident beam has varying angles, and this will allow the velocity to change depending upon different scenarios.

Also Read:

Does Refraction Change Speed: How, Why, When, Detailed facts

January 20, 2024January 22, 2022 by Keerthana Srikumar

$Does Refraction Change Speed: How, Why, When, Detailed facts 33$

Does refraction change speed? Certainly, the refraction will change speed when travelling from one medium to another.

How to know does refraction changes speed? When light travels from a rarer medium to a denser medium, the speed will change and certainly will know if the refraction ray moves towards or away from the normal.

To understand this phenomenon better, we shall use a real-world example and apply the same notions here. A cart with wheels on all its edges is kept on a concrete road. What will happen if this cart is moved to the grass area when constant force is applied to it?

When the cart is moved to the grass, the speed will increase and move in the same direction, but only if the original direction seems to be perpendicular. Otherwise, the speed may vary according to the respective direction.

Now the cart is moved from the concrete road to the grass area at an angle. We might see a change in the direction of the cart. The wheel entering the grass surface will slow down, causing the other wheel to enter the grass area too. So altogether, the wheel will move towards the right.

Now that the cart’s front wheels have different speeds compared to the ones on the concrete road. With constant speed, the cart will move in the same direction as the front wheels. This is similar to light waves in a different medium.

How does refraction change speed?

The explanation in the above section regarding the topic of refraction change speed, with the example, has given an initial viewpoint on the changing speeds in different mediums.

Now we need to deal with the following question of how does refraction change speed. Using the same example as earlier, we shall see how the process goes. When a cart is moved from the concrete road into the grass area, the speed of the cart is changed.

Similar is the case with the refraction of light if it moves from a rarer to denser medium and forms a denser to rarer medium. The refraction direction is determined when it moves towards the normal or away from the normal.

Like when we said that the wheels of the cart would lower its speed when it enters the grass area; similarly, the refraction speed will decrease when it leaves the rarer medium and enters the denser medium.

The next case is that when the cart moves from the grass area to the concrete road, the wheel will undoubtedly change its speed and move from the normal that is imaginably drawn on the surface.

Similarly, the refraction will change its speed when it enters the rarer medium after leaving the denser medium. Here also, the speed will decrease sin it is changing its direction from the original direction, that is, when it moves away from the normal to the surface.

Why does refraction change speed?

Certain factors change the speed of light in terms of refraction. Let us use the same example as earlier and understand this better.

For instance, the cart moving from the concrete road to the grass area experiences a change in speed and direction. So why does the refraction speed change? The reason is that resistance is applied to the cart’s wheels when it enters the grass area.

The grass area offers more resistance than the concrete road, so when the first wheel of the cart touches the grass due to resistance, the speed will be altered, causing the rest of the wheels to change speed.

Similarly, when the ray of light enters the denser medium from the rarer medium, the speed of refraction will change, changing the speed as well. The reason being the refractive index is different for a different medium.

The refraction changes its speed because once the light enters another medium, it will change the speed according to the medium it travels. So it will end up having a wavelength either shorter or longer based on the medium and the change in velocity.

The refractive index plays a vital role as it aids in changing the direction and the speed of the light wave. Depending on which the index will increase or decrease the speed of the light wave.

When does refraction change speed?

The word refraction itself means a change in the direction of the light wave entering one medium from another.

When the light wave enters the denser medium from the rarer medium, the first set of beams touching the denser medium will instantly change the speed. That is, the speed of the beam will decrease.

It will cause the rest of the beam to change its speed accordingly when it is entirely in the denser medium now. The surface of the medium plays a significant part in altering the speed and direction of the light wave entering.

Also, if the light beam travels in the direction perpendicular to it, the speed will increase and keep moving in the same direction as the original one. The medium in which the light travels will aid in altering the quantity, such as velocity and wavelength.

Similarly, when the light wave travels from a denser medium to the rarer medium, the speed will increase and move away from the surface’s normal. So the medium is essential for the light to travel.

If the light beam is incident the denser medium, it will move towards the normal as the speed of the beam is decreased, and when the light beam is incident on the rarer medium, the speed will increase and bend away from the normal.

1 2 — **Light beam moving towards normal**

Relationship between Speed and Refraction

Light waves been when it travels from one medium to another , and speed is the measure of how much it has been bent.

Refraction itself means the change of direction due to the change in speed of the light wave entering one medium from another medium. We can easily understand the concept using Snell’s Law n1/n2 = sin α2/sin α1, which gives an idea.

Snell’s Law is the Law that describes the relationship between the incident angle and the refracted angle of the light wave passing from one medium to another. From this, we can easily capture the relation between refraction and speed.

Refraction refers to the process when a light wave bends towards or away from the normal. When this happens, depending upon the medium, the light’s speed is described, and hence the speed and refraction are required to determine the direction of the light wave.

The change in the direction of the light wave is determined by the amount of change in speed of that light wave that enters a particular medium. Early attempts were made to study the speed of light when it travels from one medium to another.

Problems on how does refraction changes speed

There is one formula to solve any problem regarding refraction, reflection, speed and direction of any light wave entering and leaving a medium.

So here, in this case, we use the formula of Snell’s Law, which will help determine the refraction, speed, and direction. Mainly as to how does reflection changes speed.

Problem 1:

Calculate the speed of light in water when it enters the medium from the air (rarer medium). The speed of light in air is 3×10⁸, and the refractive index of the denser medium is 1.333.

Solution:

We know the relation between the speed of light in a medium and the refraction is n=c/v. We are rearranging this formula to get velocity, v=c/n.

V=c/n

V=3×10⁸/1.333

V=2.2505 x 10⁸ m/s

The speed of light in the denser medium seems to be larger than half of the speed in a vacuum.

Problem 2:

Calculate the speed of light in acetone when it enters the medium from the air (rarer medium). The speed of light in air is 3×10⁸, and the refractive index of the denser medium is 1.36.

Solution:

V=c/n

V=3×10⁸/1.36

V=2.2058 x 10⁸ m/s

The speed of light in the denser medium also decreases when it enters from the rarer medium.

Frequently Asked Questions

Why does refraction occur in water?

Refraction occurs in water because the refractive index of water is higher than in a rarer medium.

When a light beam travels from rarer and touches the denser medium, it will instantly change direction. The reason is that air is a rarer medium and water is a denser medium, which is determined by the refractive index of both mediums, respectively. Since the water is denser than air, the light wave will bend towards the normal, called refraction.

Why does light refract when it enters a different medium?

The light reflects when it enters another medium is because the refractive index of all mediums has different values.

This is also regarded as refraction. This occurs because when the light beam enters the medium and changes the speed, it changes its direction as well. In this way, we can see that if the light beam is perpendicular to the surface, there will be no change in the direction but only the speed changes.

Will the light beam bend when entering different mediums if the speed of light is constant in all mediums?

Certainly no, the light beam bends when entering a different medium only when the speed of light is different in a different medium.

If the speed of light is a constant in all mediums, there will be no bending of light waves happening. The light wave will experience a change in speed when it enters a different medium due to the value of the speed of light. The difference in speed between the two mediums is why there is a ripple on the water when the light travels from the medium of air to water.

What will happen if a light wave travels from a rarer medium to a medium with a negative refractive index?

Firstly we need to know the maturity of light, whether it is a particle or a wave.

The magnitude value of velocity is regarded to be the speed. Speed cannot be negative, and when we consider the velocity, it certainly cannot be negative. The answer to this question is mainly practicality. If the light is a wave, then depending upon the light’s phase velocity, we must conclude. Refractive index is a ratio of two quantities there is no question for it to be positive or negative.

Also Read:

How to Find Resultant Force of Two Forces: Problem and Examples

January 21, 2024January 20, 2022 by Keerthana Srikumar

When dealing with forces in physics, it is often necessary to find the resultant force of two or more forces acting on an object. The resultant force is the single force that can replace multiple forces and have the same effect on the object. In this blog post, we will explore how to find the resultant force of two forces, as well as how to calculate the resultant force of multiple forces using mathematical equations and principles.

III. The Mathematical Approach to Finding Resultant Force

how to find resultant force of two forces — Image by Cleontuni – Wikimedia Commons, Wikimedia Commons, Licensed under CC BY-SA 3.0.

A. The Resultant Force Equation

To find the resultant force of two forces, we can use the equation:

$\text{Resultant Force} = \sqrt{{F_1}^2 + {F_2}^2 + 2F_1F_2\cos{\theta}}$

Where ( F_1 ) and ( F_2 ) are the magnitudes of the two forces, and ( theta ) is the angle between them.

B. The Formula for Resultant Force

Another formula that can be used to find the resultant force is derived from the law of cosines. It is given by:

$\text{Resultant Force} = \sqrt{{F_1}^2 + {F_2}^2 + 2F_1F_2\cos{(180^\circ - \theta)}}$

This formula is particularly useful when the angle between the forces is obtuse (greater than 90 degrees).

IV. How to Calculate the Resultant Force of Two Forces

A. Step-by-Step Guide to Calculating Resultant Force

To calculate the resultant force of two forces, follow these steps:

Identify the magnitudes and directions of the two forces.
Determine the angle between the forces.
Use either the resultant force equation or the formula derived from the law of cosines to calculate the resultant force.

B. Worked Out Example: Calculating Resultant Force of Two Forces

Let’s consider an example to better understand how to calculate the resultant force. Suppose we have two forces: ( F_1 ) with a magnitude of 10 N acting at an angle of 30 degrees, and ( F_2 ) with a magnitude of 8 N acting at an angle of 60 degrees.

Using the resultant force equation, we can calculate the resultant force as follows:

$\text{Resultant Force} = \sqrt{{10}^2 + {8}^2 + 2 \cdot 10 \cdot 8 \cos{30}}$

Simplifying the equation, we get:

$\text{Resultant Force} = \sqrt{100 + 64 + 160 \cos{30}}$

$\text{Resultant Force} = \sqrt{100 + 64 + 80}$

$\text{Resultant Force} \approx \sqrt{244} \approx 15.62 \, \text{N}$

Therefore, the resultant force of the two forces is approximately 15.62 N.

V. How to Determine the Resultant Force of Two Vectors at an Angle

Image by en:User:Cleonis – Wikimedia Commons, Licensed under CC BY-SA 3.0.

A. Understanding the Role of Angles in Resultant Force

When the two forces are not acting along the same line, it is essential to consider the angle between them. The angle affects the magnitude and direction of the resultant force. If the forces are acting in the same direction, the angle is 0 degrees, and the resultant force is the sum of the two forces. If the forces are acting in opposite directions, the angle is 180 degrees, and the resultant force is the difference between the two forces.

B. Step-by-Step Guide to Calculating Resultant Force of Two Vectors at an Angle

To determine the resultant force of two vectors at an angle, follow these steps:

Resolve the forces into their horizontal and vertical components.
Add the horizontal components and the vertical components separately.
Use the Pythagorean theorem to find the magnitude of the resultant force.
Use trigonometry to find the angle of the resultant force.

C. Worked Out Example: Calculating Resultant Force of Two Vectors at an Angle

Let’s consider an example to illustrate how to calculate the resultant force of two vectors at an angle. Suppose we have two vectors: ( vec{F_1} ) with a magnitude of 10 N at an angle of 30 degrees, and ( vec{F_2} ) with a magnitude of 8 N at an angle of 60 degrees.

Using trigonometry, we can calculate the horizontal and vertical components of each vector:

$( \vec{F_1} )$ horizontal component: $( 10 \cos{30} )$ N
$( \vec{F_1} )$ vertical component: $( 10 \sin{30} )$ N

$( \vec{F_2} )$ horizontal component: $( 8 \cos{60} )$ N
$( \vec{F_2} )$ vertical component: $( 8 \sin{60} )$ N

Next, we add the horizontal components and the vertical components separately:

Horizontal component of resultant force: $( 10 \cos{30} + 8 \cos{60} )$ N
Vertical component of resultant force: $( 10 \sin{30} + 8 \sin{60} )$ N

Using the Pythagorean theorem, we can find the magnitude of the resultant force:

$( \text{Magnitude of resultant force} = \sqrt{{(\text{horizontal component})}^2 + {(\text{vertical component})}^2} )$

$( \text{Magnitude of resultant force} = \sqrt{{(10 \cos{30} + 8 \cos{60})}^2 + {(10 \sin{30} + 8 \sin{60})}^2} )$

Simplifying the equation, we get:

$( \text{Magnitude of resultant force} \approx \sqrt{{(10 \cdot 0.866 + 8 \cdot 0.5)}^2 + {(10 \cdot 0.5 + 8 \cdot 0.866)}^2} )$
$( \text{Magnitude of resultant force} \approx \sqrt{{(8.66 + 4)}^2 + {(5 + 6.928)}^2} )$
$( \text{Magnitude of resultant force} \approx \sqrt{{12.66}^2 + {11.928}^2} )$
$( \text{Magnitude of resultant force} \approx \sqrt{{160.0756 + 142.185984}^2} )$
$( \text{Magnitude of resultant force} \approx \sqrt{302.261584} \approx 17.39 \, \text{N} )$

To find the angle of the resultant force, we can use inverse trigonometric functions:

$( \text{Angle of resultant force} = \arctan{\left(\frac{\text{vertical component}}{\text{horizontal component}}\right)} )$

$( \text{Angle of resultant force} = \arctan{\left(\frac{10 \sin{30} + 8 \sin{60}}{10 \cos{30} + 8 \cos{60}}\right)} )$

Simplifying the equation, we get:

$( \text{Angle of resultant force} = \arctan{\left(\frac{5 + 6.928}{8.66 + 4}\right)} )$
$( \text{Angle of resultant force} = \arctan{\left(\frac{11.928}{12.66}\right)} )$
$( \text{Angle of resultant force} \approx \arctan{0.942} )$
$( \text{Angle of resultant force} \approx 43.65^\circ )$

Therefore, the resultant force of the two vectors is approximately 17.39 N at an angle of 43.65 degrees.

VI. Advanced Calculations: Finding the Resultant Force of Multiple Forces

A. How to Calculate the Resultant Force of Four Forces

When dealing with multiple forces, we can find the resultant force by applying the parallelogram law of vector addition. This law states that if two vectors are represented in magnitude and direction by the sides of a parallelogram, then the resultant vector is represented in magnitude and direction by the diagonal of the parallelogram drawn from the same starting point.

To calculate the resultant force of four forces, follow these steps:

Draw a vector diagram, representing the magnitudes and directions of the four forces.
Complete the parallelogram using the given forces as adjacent sides.
The diagonal of the parallelogram represents the resultant force.
Measure the magnitude and direction of the diagonal using a ruler and protractor.

B. Worked Out Example: Calculating Resultant Force of Four Forces

Let’s consider an example to illustrate how to calculate the resultant force of four forces. Suppose we have four forces with magnitudes of 5 N, 8 N, 10 N, and 12 N, acting at angles of 45 degrees, 90 degrees, 135 degrees, and 180 degrees, respectively.

Using a vector diagram, we can represent these forces as arrows:

Completing the parallelogram using the given forces, we find that the diagonal represents the resultant force.

Measuring the magnitude and direction of the diagonal, we can determine the resultant force. Let’s assume that the magnitude is approximately 16 N, and the direction is 30 degrees above the positive x-axis.

Therefore, the resultant force of the four forces is approximately 16 N at an angle of 30 degrees.

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Centripetal Force vs Centripetal Acceleration: Comparative Analysis

January 21, 2024January 18, 2022 by Keerthana Srikumar

Centripetal force vs centripetal acceleration is the one related to a circular motion in general. They are the main reason for a body undergoing circular motion.

CENTRIPETAL FORCE	CENTRIPETAL ACCELERATION
It is the force required to move in circular path	It is the acceleration required when velocity is changed
It is provided by the normal force	It is provided by the change in velocity
It is directed towards keeping the object in circular motion	It is directed towards the axis of rotation

centripetal force vs centripetal acceleration

Motion can be categorized in several different aspects, and one such being is the circular motion. Velocity, acceleration and force are required to drive the body in motion be it linear or circular.

But one needs to know the difference between the linear motion and circular motion that drives the body at a particular direction. Hence centripetal force vs centripetal acceleration is a combination of quantities that aid in the motion of a body in the circular motion.

In this article we will be discussing the difference and similarities of centripetal force vs centripetal acceleration. Any system that is under motion will need a force that pushes the body to be in the same until and unless an external force is applied.

Centripetal force is the required force which helps the body to go around in circular paths. There exists normal force too in any motion of the system. This normal force also keeps the mass of the body intact.

The normal force provides a force to the system to go move in circular motion which is called as the centripetal force. The magnitude of the normal force in curvatures is different form the normal force that is presented in system that is in linear motion.

centripetal force vs centripetal acceleration — **“Centripetal-Force-Problems-Quiz—PPB” by Zappy’s is licensed under CC BY 2.0**

Centripetal Force Insights

Now let us dive deep into the discussion as to how the centripetal force is been exerted on the body under motion and how centripetal acceleration aids to that motion as well.

Let us say a car is moving straight on road with normal force and acceleration. Now there is a curve to pass through and what will be the force and acceleration that aids in passing through the curves. If the direction changes there certainly will be a change in the value of magnitude.

The answer to this is simple, that is, when the car is in linear motion the force exerted on the car is considered to be normal. This exertion of normal force is given by the road on the surface of the car.

The normal for is responsible for the motion in curved are because it the one providing the centripetal force for that curved motion. When the normal force provides another force to the car in order to move in circular path then that is called as the centripetal force.

Generally centripetal force is given by the static friction that’s aid in circular motion of an object. The normal force in the curved path is greater than the one in straight path. Here the magnitude will face so many changes in the values in order to change the direction.

2 2 — **“Centripetal-Force-Problems-Discussion-Questions” by Zappy’s is licensed under CC BY 2.0**

Centripetal Acceleration Insights

Before we discuss the centripetal acceleration we need to know about the velocity factor and what drives it to the acceleration part.

The velocity in curved path is required to drive the object further down the path. When the speed is altered there will surely be acceleration aiding the motion. Centripetal acceleration is the one which has so many other factors are been included.

Time period and frequency are been considered when we take into account of the centripetal acceleration. Frequency in a circular path is the number of revolutions made by the object and the time period one such revolution is given the reciprocal of frequency.

In any circular motion the distance or displacement is given by the circumference of that circular path. So we consider the radius and the velocity with which the object travels the circular path.

We can easily find the centripetal acceleration in order to determine the various factors of the circular motion. Centripetal acceleration is the velocity divided by the radius and when the velocity is doubled the centripetal force is quadrupled.

Centripetal Force vs Centripetal Acceleration Formula

Centripetal force formula is given by the mass, velocity and the radius.

f_c= m v²/ r

Where fc = centripetal force; m=mass; v= velocity; r= radius.

We must be aware of the fact that this formula is something that is similar to the conventional formula of the force. This formula is similar to the one where Newton’s Second Law provides, a product of acceleration and mass.

The tangential acceleration that occurs in the curved path is also known sometimes as the centripetal acceleration. The formula for centripetal acceleration is given as,

a_c= v²r

Where ac is the centripetal acceleration; v= velocity; r= radius.

In a circular path where a body moves with a particular velocity we take into consideration of the revolution that body makes in a particular period given. The frequency is nothing but the number revolutions made.

Frequently Asked Questions

What is the formula for centripetal acceleration in vector form?

The centripetal acceleration in vector formula is simply the conventional formula.

The formula is given as ac=v2r. Expanding this formula we get the result as ac=rω2. Here ω indicated the angular frequency as it gives the number of rotations made by the object in the circular motion. The circumference if the circular path gives the distance in order to calculate the centripetal acceleration from which we can derive the value for radius.

When does centripetal component of acceleration arise in a system?

The centripetal component acceleration in a system arises when the velocity is changed.

Normally when the body travels in the circular path it will take different directions which in turn change the magnitude too. A vector quantity will have a magnitude value and direction value so does the velocity.

What is centrifugal force?

Force that pulls away from centre is centrifugal force.

When any object is pulled from the center of its circular path by action of a force is called the centrifugal force. Hence this force pulls the body away from the center point in the curved path.

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