Category: Physics Notes PPT

Wave Velocity is one of the common topics of all the exams that test students on the parameters of physics. Students normally find it hard to deal with this topic as it is a little complex in nature. Although, if studied well, the same topic could be very scoring for the students from exam point of view. To bridge the gap between students and their learning has come up with an article prepared by a team of dedicated teachers on wave velocity.  Wave Velocity – Formula, Properties, Examples could also be found in the PDF format from the website. The students can download it on their devices and study from the comfort of their homes. The resource is free of cost and doesn’t require any prior registration fee. 

A wave is a result of external perturbation in a plane surface. We can define a wave as – a wave is a disturbance propagating in space with transportation of energy and momentum from one point to another without transfer of the matter. The most commonly used examples for waves are the ripples in a pond, Sound that reaches us propagates through wave motion, TV signals, etc.  The waves are classified into different types depending upon the type of medium, propagation energy, dimensions, and the vibration of particles.

What is Wave Velocity?

Now, we are constantly talking about the term wave velocity. To understand the wave velocity first, let us look at the meaning and define wave velocity.

• The wave velocity definition is given as the velocity associated with the disturbance propagating in the given medium or in other words, wave velocity is the distance traveled by waves per unit time.

• The wave velocity depends upon the nature of the medium used.

• The wave velocity is also known as phase velocity  

Now the formula of wave velocity is given as follows. The wave velocity formula says it is the product of wavelength and the frequency of the wave. I.e.,

Wave velocity (v) mathematically is given by,

[Rightarrow v = frac{w}{k} ]……….(1)

 Where,

 w – The angular velocity

 k – the angular wavenumber or propagation constant

We know that,

The value of the angular velocity = w =  [2pi nu ]; where [nu] – Frequency of the wave

The value of the wavenumber = k = [frac{2pi}{lambda}]; where [lambda] – The wavelength

 Substituting these value in equation (1) we get,

 [Rightarrow = frac{2pinu}{2pilambda} = lambdanu  ]

Therefore, we have,

[Rightarrow =  v = lambdanu ]…….(2)

Where,

[lambda]- The wavelength

[nu] – Frequency of the wave

Equation (2) is known as the equation of wave velocity or wave velocity formula.

Wave Velocity Formula:

In wave motion, the perturbations travel through the medium due to repeated periodic oscillations of the particles. The velocity of the wave will be different from the velocity of the particles with which they vibrate about their mean positions. The wave velocity will always be constant but the particle velocity will be changing with time periods.

Properties of Wave Velocity:

The wave velocity in a given medium is always constant.

The wave velocity is independent of the time and source of the wave, but the wave velocity depends on the wavelength of the propagating wave in a given medium.

The wave velocity depends on the medium used.

Examples:

1. How to Calculate Wave Velocity for a Given Periodic Wave with a Wavelength of 3m Has a Frequency 6Hz?

Sol: Given,

The wavelength of the periodic wave = [lambda] = 3m

The frequency of the given periodic wave = [nu] = 6Hz

We have to calculate the wave velocity of the given periodic wave. From the equation of wave velocity we have,

[Rightarrow v = lambdanu ]

Where, 

[lambda] – The wavelength

 [nu]  – Frequency of the wave

Substituting the corresponding values in equation (1) we get, 

[Rightarrow]  v = (3)(6) = 18 m/s 

Therefore, the wave velocity of a given periodic wave is 18 m/s.

2. How Do You Find the Velocity of a Wave with a Wavelength of 20m has a Frequency 70Hz?

Sol: Given,

The wavelength of the periodic wave = [lambda] = 20m

The frequency of the given periodic wave = [nu] = 70Hz

We have to calculate the wave velocity of the given periodic wave. From the equation of wave velocity we have,

[Rightarrow v = lambdanu ]

Where, 

[lambda] – The wavelength

 [nu]  – Frequency of the wave

Substituting the corresponding values in equation (1) we get, 

⇒ v = (20)(70) = 1400 m/s

Therefore, the wave velocity of a given periodic wave is 1400 m/s.

3. The Velocity of Wave 70m/s. If the Wavelength of the Wave is 1m then Calculate the Frequency of the Given Wave.

Sol: The wavelength of the wave = [lambda] = 1m

The wave velocity of the given wave = v = 70m/s

We have to calculate the Frequency of the given wave. From the equation of wave velocity we have,

[Rightarrow v = lambdanu ]…… 1

Where, 

[lambda] – The wavelength

 [nu]  – Frequency of the wave

On rearranging the equation (1) for the frequency of the wave, 

[Rightarrow nu = frac { v}{λ} ]……(2) 

Substituting the given values, 

[Rightarrow  nu = frac {70}{1} ]……(2) 

 = 70 Hz

Therefore, the frequency of the given wave is 70Hz 

4. A Wave with a Frequency 450Hz is Traveling at a Speed of 200m/s. Then Calculate the Wavelength of the Wave. 

Sol: The frequency of the wave = [nu] = 450Hz

The wave velocity of the given wave = v = 200m/s 

We have to calculate the wavelength of the given wave. From the equation of wave velocity we have,

[Rightarrow v = lambdanu ]…… 1

Where, 

[lambda] – The wavelength

 [nu]  – Frequency of the wave

On rearranging the equation (1) for the wavelength of the wave, 

[Rightarrow lambda = frac { v}{nu} ]………(2) 

Substituting the corresponding values in (2) we get, 

[Rightarrow  lambda = frac {200}{450} ]………(2)

 = 0.44m 

Therefore, the wavelength of the given wave is 0.44m.

 

Revision remedy

The Wave Velocity – Formula, Properties, Examples article developed by is a perfect tool for revision for the students. It is advised that when the exams are near, you should choose to revise from the wave velocity PDF. The article precise
ly mentions all the details with complete clarity to the students. One may even choose to make notes from the above content and enhance her chances to score well in the exams.  On the other hand, just underlining the keywords would suffice too. All one has to do is look at the keywords.  If feasible, taking a printout is also a convenient idea.

Making the Notes and Underlining 

As it is common knowledge, having good revision notes is the best policy for scoring well in exams.  One can use the wave velocity article to make the revision notes. Note down all the keywords and important definitions that are relevant from the exam point of view. 

The scattering of light is an important part of our daily life, although we didn’t realize its importance. Scattering of light is different from reflection, as in reflection the radiation is deflected in one direction while in scattering every object or particle can scatter light and illuminates them in all directions. When a parallel beam of light passes through any particle present in air or gas; the particles present in the air scatter the light beam in all directions besides its incident direction. This phenomenon of, light striking the particles present in the air and after absorbing some light it radiates it in different directions except its incident direction, is called as “Scattering of light”. The loss of energy in a light beam after scattering can be calculated by the strength of scattering, its value depends on the wavelength of the light and the size of the particle which causes scattering. 

This process of scattering of light can also be shown with the help of an example of light rays falling from the sun, as when the rays of the sun enter the earth’s atmosphere there are various small particles present in the air. These particles collide with the sun rays falling and while absorbing some light making them scatter/ deflect in different directions besides its incident direction. Basically, we can say that a ray of light is deflected from its straight path due to some irregularities present in the medium, particles, or due to the interference between the two media.

When the light passes from one medium, say water, to another medium, say air, some of the light is absorbed by the first medium before it scatters into the second medium. The amount of light absorbed in the first medium and the amount of light scattered varies based on the wavelength and intensity of the light. When the wavelength of the light ray is less, it has more waves and the chance of light particles colliding with the other particles in the medium are more. So the scattering of light is generally more. On the other hand, when the wavelength of the light ray is more, the frequency of the wave is less and there are fewer chances of light particles getting scattered.

There are several ways how the scattering of light takes place, but two main examples are:-

Random Reflection from a Rough Surface

All surfaces are rough; the roughness of the surface is related to the wavelength of the light ray. As the surface has more roughness absorbs more energy from the light ray and will scatter it in different directions depending on the wavelength of the light ray. The rough surface of a car or pieces of jewelry can be taken as a good example of scattering through a rough surface.

Reflection Through Impurities present in Volume

This type of scattering through impurities present in the volume helps in the medical types of equipment. Thompson mechanism, which is also known as elastic scattering, is a good example of this type of scattering which is used in medical X-ray photographs. This type of scattering occurs where light is scattered by charged particles by leveling the energy of the incident radiation and the rest energy of the charged particle present. The passing of light rays through any liquid in which light beam scatters only with the tiny fat droplets is a good example of this type of scattering.

Single and Multiple Scattering

When the scattering of light takes place with only a single localized scattering center then the phenomenon is known as single scattering, it is generally treated as a random phenomenon as it has only a single scattering center that can do a single scattering event at a particular time. While that scattering takes place with many localized scattering centers, a large number of localized centers involves a large number of combined results which give more number of scattered light to the observer. The single type of scattering is not always random, as they can be intentional sometimes in the case of a laser beam, which can be well controlled for scattering to a single point for an instance, along with the radar scattering where the targets tend to be microscopic in size.

Types of Scattering of Light

1. Rayleigh or selective scattering

2. Mie scattering

3. Electromagnetic scattering

Rayleigh or Selective Scattering

Rayleigh scattering of light is a type of elastic scattering as the particle from which the scattering has to be done depends on the wavelength of light. Depending on the wavelength, certain particles are more effective than others which scatter light having more wavelength, as the particles like molecules of oxygen, nitrogen having small size scatter light with a shorter wavelength (blue or violet) in different directions. The blue sky on a clear sunny day is also the result of Rayleigh scattering by the air molecules. 

The blue light having a shorter wavelength appears to scatter from the upper atmosphere about 10 times which is much larger than the red light having a larger wavelength. Hence, the blue light having a shorter wavelength collides with the air molecules and is scattered to the eyes seeing the sky, making it blue. On the other hand, the red light with a higher wavelength goes largely unscattered to the sky. Scattering of optical signals through optical fibers is also included in this type of scattering.

Mie scattering

Mie scattering is also a type of elastic scattering mechanism, in which the size of the molecules is greater than the wavelength of the light which results in the non-uniform scattering of light. This type of scattering is not much dependent on wavelength as the size of the molecule which scatters light is more important. Due to this process, the clouds having water droplets look white. 

The scattering efficiency of the small molecules becomes less in the atmosphere with the wavelength of the white light. This shows that the light ray which enters the clouds get scattered by water droplets for all wavelength and no light of visible wavelength is left in the cloud making the cloud look white. When the clouds become full of water droplets no light is taken in the cloud for scattering making it looks darker. The light rays falling on the earth’s surface results in different types of scattering, making the color of the sky blue and making the color of the clouds white. The white color of fog and clouds both are the results of “Mie scattering”.

Electromagnetic Scattering

It is the most common form of scattering as it includes electromagnetic waves. It generally includes two types of scattering which are elastic light and inelastic light scattering. Elastic light scattering includes Rayleigh scattering or Mie scattering while inelastic scattering includes Raman scattering, inelastic x-ray scattering, Compton scattering, and Brillouin scattering.

The intensity of the light scattered from the molecules generally depends on two factors which are the wavelength of the light to be scattered and the size of the molecules due to which the light falling on the earth’s surface is scattered. The light ray falling on the earth’s surface having a shorter wavelength and high frequency tend to scatter more because of the intersection with the particles a
nd the waviness of the line. While the light rays falling on the earth’s surface having a low frequency and longer wavelength tend to scatter less because they move in a straighter path which makes the possibility of colliding with the particles less.

The probability of scattering and λ the wavelength of the light can give the relation as follows:

[Palpha frac{1}{lambda ^{4}}]

Where P is the probability of scattering

And, λ is the wavelength of the light.

The above relation between the probability of scattering and the wavelength of the light shows that the probability of scattering is inversely proportional to the fourth power of the wavelength and the probability of scattering will be higher for the shorter wavelength of the light.

We all have heard about wind turbines, and many of us might also have seen them. So, how does a wind turbine make energy, and how does such a massive machine generate electricity from the wind, which doesn’t feel to be so forceful or effective. Well, today we are going to find out answers to all these questions. But first, we need to talk about how a wind farm works and the principle behind the wind turbine generator? 

From massive wind farms that generate kilowatts of electricity each day to a single vertical axis wind turbine at the farmhouse, all work on the same principle of current alternative production. Turbines attached to the blades are placed high above the ground, and most of them have three blades attached to them. When the wind blows, these blades move, and a pocket of low-pressure air forms one side of the blade. This low pressure pulls the blade towards it, making the rotor turn. This phenomenon is known as a lift in wind power turbines. The force that the lift puts on the blade is much stronger than the force put by the wind against the other side of the blade, known as drag. The perfect combination of drag and lift causes the rotor to propel at a much faster speed. 

Inside Wind Power Turbines

Now let’s talk about what’s inside the wind power turbines. Inside a wind turbine, we have a series of gears that increase the rotor’s rotation from above 18 revolutions a minute to roughly 1800 revolutions per minute. These 1800 revolutions cause the turbine to generate alternating current electricity. All the turbine components are stored in one location, which is called a nacelle, and it includes all the gears, rotors, and generators. You might be surprised to know that, but some turbines have such a massive nacelle that even a helicopter can land on them. 

Different Types of Wind Turbines

Two different forms make the wind power plants of wind turbines, and we will explain each of them in this section. 

Horizontal-axis Turbines 

If you look at the horizontal-axis turbines, you will see they are more like an airplane propeller and have three blades in them. The largest air turbine stands tall at the height of a 20 story building, and the blades are 100 feet long. Nearly all the wind power turbines which you see today are horizontal-axis turbines. 

Vertical-axis Turbines 

These turbines have blades that are attached at the top and the bottom of the vertical rotor. The most common type of vertical wind turbine is the Darrieus wind turbine, named after the engineer who invented it. If you look at this turbine from a distance, it will look like a massive two-bladed egg beater. Some of the vertical-axis turbines are 100 feet tall, and others could be 50 feet depending on the location in which they are installed. In the modern age, there are only a few places where you can find a vertical-axis turbine making electricity as electricity production is low. They do not perform as well and efficiently as horizontal-axis turbines. 

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Use of Wind Energy

• The first and the foremost use of wind energy is to generate clean electricity with big and small wind turbines. 

• The second is transportation; for many years, people were using sails to travel the world; before there were diesel engines to make the ships move, humans took the assistance of wind energy to traverse the sea. On the other hand, modern shipping companies are researching ways to use wind energy for their transportation as it is a free and clean form of energy.

• Wind energy is also used for wind sports, such as windsurfing, land sailing, kitesurfing, etc. 

Conclusion 

Now you know how wind generators produce electricity and the different types of wind power turbines. Wind power is not something new, and as a civilization, we have been harnessing it for our users for quite a few centuries now. In the next ten years, wind energy will be more efficient, and more wind farms will be set up to take advantage of a renewable resource. 

Yield strength is defined as the property of a material and the amount of stress corresponding to a yield point where the material automatically begins to disfigure and takes a plastic form. The yield strength is used to find out the extreme allowable load that a mechanical component can bear. It represents the upper limit of the force that can be applied to a material without resulting in its permanent deformation. Yielding is, thus, a failure mode and is not catastrophic. Like the tensile strength, the yield strength is calculated in Pascals (Pa) or Megapascals (MPa). The yield strength of mild steel is approximately 250 MPa. 

Strength Tensile 

Tensile strength refers to the measurement of a force that is needed to pull an object like a structural beam, wire, or rope to the extreme point where it eventually breaks. The tensile or yield strength of a material is the highest amount of tensile stress that it can take before breaking into small pieces. Tensile ultimate strength refers to the highest stress that a material can withstand before breaking down. 

Steel Tensile Strength 

Tensile, by its meaning, refers to the ability of steel drawn out. Tensile strength is the resistance power of the steel to break under the tensile strain. It is used in specifying the point where the steel transforms from an elastic form to a plastic form. It is usually measured in the unit of force per cross-section of an area. Once the steel is pulled from its stress point, it splits apart. 

Tensile Strength of Mild Steel

Tensile strength is the maximum amount of stress that any material can withstand when pulled or stretched. Any tensile strength undergoes a test that includes taking samples of a material with a fixed area of the cross-section by putting it inside a tensometer that increases its force till it breaks. 

Few materials break down without deforming, while materials that are more ductile, stretch only a little and shrink at a point where stress is extreme. Tensile strength is thus measured as a force per unit of the area measured in Pascal, pounds per square inch, or Megapascal. 

Thus, mild steel is a less ductile material because it has small amounts of hardening alloy and carbon than other steels. It has a relatively slow tensile strength of 400MPa.

Yield Stress of Steel 

Yield strength refers to the extreme strength that is applied to an object before it results in changing the shape and structure of the object. The strength of any material is determined by a test called the tensile test. In this test, the particular material is stressed and pulled strongly from both directions. From this test, a graph can be drawn that can also be called a stress-strain graph. 

The Stress-Strain Graph has some particular features. These include the following:

The graph has a different region or points such as:

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1. Proportional Limit: This is the place in the stress-strain curve where Hooke’s Law is maintained. Thus, the ratio of the stress about the strain gives a proportionality constant that is called Young’s modulus. The point OA in the stress-strain graph is known as the proportional limit.

2. Elastic Limit: This is the point where the particular material returns to the original point as soon as the load acting on the body is finally removed. After reaching this limit, the material does not return to the original point and thus a plastic deformation takes place on the material.

3. Yield Point: The yield point is the point where the material finally starts to deform in its state and generally turns into plastic. After the point is passed, a permanent deformation takes place in two forms. One can be a lower yield point and the other can be an upper yield point. 

4. Ultimate Stress Point: It is the final point that shows the maximum stress that the material can withstand before deforming. If the material goes beyond this point then failure occurs. 

5. Breaking or Fracture Point: It is the point that shows the failure of the material. 

Aluminium yield strength 

6061 aluminium alloy contains a yield tensile strength of 276 MPa (40000 psi) as well as an ultimate tensile strength of 310 MPa (45000 psi).

The measure of the force of gravity that is acted upon a body is known as its weight. It is denoted by w. In mathematical terms, weight can be described as the product of mass and acceleration due to gravity.

W = mg

Since weight is considered a force, its SI unit is also considered as the same as that of force which is Newton (N). The weight of a body is dependent on two factors, according to the expression of weight, which are the mass which is constant, and acceleration due to gravity which might differ in different places.

What is Mass?

The mass of a body can be defined as the measure of the amount of matter that is present inside the body. Its SI unit is kilograms (kg). For a given body, the mass rarely changes for any given time. However, if a large amount of energy is taken out or given to the body, there may be a change in the mass of the body. For an instance, in the case of a nuclear reaction, a huge amount of energy is converted from a very little amount of energy which results in the reduction of mass of the substance.

Calculation of Weight from Mass

Suppose a body possesses a large mass and a large weight and this body is a very large object that is hard to throw because of its weight.

Therefore by using Newton’s second law which states that the magnitude of the acceleration is ‘g’ for an object which is freely falling.

Therefore, if the mass of an object is 1 kg which is falling with an acceleration of 9.8 ms⁻², the magnitude of the force will be given by-

F = ma

F =(1 kg) x (9.8 ms⁻²)

F = (9.8 kg.ms⁻²)

F = 9.8 N

Hence, it is clear that for an object with mass m= 1 kg, the weight of the object will be equal to 9.8 N.

Examples:

Question: For a freely falling object of mass 10Kg, an upward force of 20N is applied. Find the final acceleration. (g = 10 [frac{m}{s^{2}}])

Ans:

Net downward force = weight of the object = 100 N

Net upward force = 20N

Net force = 80N in the downward direction.

So, Net acceleration = [frac{80}{10}] = 8Kg

Question: What will be the weight of an object on the moon, if its weight is 90N on earth.

Ans: Weight of an object on earth = 90N

Weight of object on moon =?

We know that gravitational force on the moon is equal to one-sixth of earth’s gravitational force.

Weight of a body on earth, [W_{earth}] = [mg_{earth}]

Weight of a body on the moon, [W_{moon}] = [mg_{moon}] == [frac{mg_{earth}}{6}] = [frac{W_{earth}}{6}] = [frac{90}{6}] = 15N

Conclusion 

This is how weight is defined and its formula is derived. Learn how the terms are used to define the concept and to calculate the weight. Find out the relation of mass with weight.

The flow of charge is very important for determining the electric field. They have a collection of electric charges. and thus charge density is very important to calculate for many purposes. The charge density is calculated based on the surface area and the volume of the electric object. The charge density formula is a very interesting and important topic.

The charge density is the measure of the accumulation of electric charge in a given particular field. The following are some of the dimensions in which the charge density is measured:

• Linear Charge Density: [lambda = frac{q}{l} ] , where q is the charge and l is the length over which it is distributed. The SI unit will be Coulomb m^-1.

• Surface Charge Density: [ sigma = frac{q}{A}] where, q is the charge and A is the area of the surface. The SI unit is Coulomb m^-2.

• Volume Charge Density: [ rho = frac{q}{V}] where q is the charge and V is the volume of distribution. The SI unit is Coulomb m^-3.

Charge density is based on the distribution of electric charge and it can be either positive or negative. The measure of electric charge per unit area of a surface is called the charge density.

Example Problems

1. A long thin rod of length 50 cm has a total charge of 5 mC uniformly distributed over it. Find the linear charge density.

Solution:

q = 5 mC = 5 × 10^–3 C, l= 50 cm = 0.5 m. λ= ?

[lambda = frac{q}{l} ]

[= frac{(5 times 10^{-3} )} {0.5} ]

[= 10^{-2} Cm^{-1} ]

2. A cuboidal box penetrates a huge plane sheet of charge with uniform surface charge density 2.5× 10^–2 Cm^–2 such that its smallest surfaces are parallel to the sheet of charge. If the dimensions of the box are 10 cm × 5 cm × 3 cm, then find the charge enclosed by the box.

Solution:

Charge enclosed by the box = charge on the portion of the sheet enclosed by the box.

The area of the sheet enclosed; A = area of the smallest surface of the box 

[= 5 cm × 3 cm = 15 Cm^{2} = 15times 10^{-4} m^{2} ]

Charge density; [sigma = 2.5 times 10^{-2} Cm^{-2} ]

Charge enclosed; q= [sigma] A =2.5 [times] 10⁻² [times]15 [times]10⁻⁴ 

= 37.5 [times]10⁻⁶

C = 37.5 μC