Category: Physics Notes PPT

Before we learn how to calculate the pressure of an ideal gas let us first know what exactly an ideal gas is. An ideal gas in simple words is a theoretical gas in which the gas particles move randomly and there is no interparticle interaction. An ideal gas doesn’t exist in reality. It follows the ideal gas equation which is a simplified equation we will learn further and is susceptible to analysis under statistical mechanics. At standard pressure and temperature conditions, most gases are taken to behave as an ideal gas. As defined by IUPAC, 1 mole of an ideal gas has a capacity of 22.71 litres at standard temperature and pressure.

Failure of Ideal Gas Model

At lower temperatures and high pressure, when intermolecular forces and molecular size become important the ideal gas model tends to fail. For most of heavy gases such as refrigerants and gases with strong intermolecular forces, this model tends to fail. At high pressures, the volume of a real gas is often considerably larger than that of an ideal gas and at low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point in low temperature and high-pressure real gases undergo phase transition which is not allowed in the ideal gas model. The deviation from the ideal gas model can be explained by a dimensionless quantity, called the compressibility factor (Z).

Ideal Gas Equation

Ideal gas law gives an equation known as the ideal gas equation which is followed by an ideal gas. It is a combination of the empirical Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. The ideal gas equation in empirical form is given as

PV=nRT

where P= pressure of the gas (pascal)

V= volume of gas (liters)

n= number of moles of gas (moles)

R= universal or ideal gas constant ([=8.314JK^{-1}mol^{-1}])

T= absolute temperature of the gas (Kelvin)

Ideal gas law is an extension of experimentally discovered gas laws. It is derived from Boyle’s law, Charles law, Avogadro’s law. When these three are combined, we get an ideal gas law.

Boyle’s law =>  PV = k

Charle’s law => V = kT

Avogadro’s law => V = kn

Now, when we combine these three laws we use the proportionality constant ‘R’, which is the universal gas constant and we get the ideal gas equation as

V = RTn/P

=> PV = nRT 

Ideal Gas Model Assumptions

Various assumptions are made in the ideal gas model. They are as follows:

• Gas molecules are considered as indistinguishably very small and hard spheres.

• All motions are frictionless and the collisions are elastic, that is there is no energy loss in motion or collisions.

• All laws of Newton are applicable.

• The size of the molecules is much smaller than the average distance between them.

• There is a constant movement of molecules in random directions with distributed speeds.

• Molecules don’t attract or repel each other apart from point-like collisions with the walls.

• No long-range forces exist between molecules of the gas and surroundings.

The Pressure of an Ideal Gas: Calculation

For the calculation let us consider an ideal gas filled in a container cubical in shape. One corner of the container is taken as the origin and the edges as x, y, and z axes. Let [A_{1} and A_{2}] be the parallel faces of the cuboid which are perpendicular to the x-axis. Suppose, a molecule is moving with velocity ‘v’ in the container and the components of velocity along three axes are [V_{x}, V_{y} and V_{z}]. As we assume collisions to be elastic when this molecule collides with face [A_{1}] x component of velocity reverses while the y and z component remains unchanged.

Change in the momentum of the molecule is 

[Delta P= -mv_{x} -mv_{x}  = -2mv_{x} ….. (1)]

The change in momentum of the wall is [2mv_{x}] as the momentum remains conserved.

After the collision, the molecule travels towards the face [A_{2}] with the x component of the velocity equal to [-v_{x}] 

Now, the distance traveled by a molecule from [A_{1}] to [A_{2}] = L

Therefore, time = [ frac{L}{v_{x}}]

After a collision with [A_{2}] it again travels to [A_{1}]. Hence, the time between two collisions= [ frac{2L}{v_{x}}]

So the number of collisions of molecule per unit time [n = frac{v_{x}}{2L}]……….(2)

From (1) and (2),

Momentum imparted to the molecule by the wall per unit time

∆F=n∆P

 [ = sum frac{m}{L *  v_{x}^{2}}]

Therefore, the total force on wall  [A_{1}] due to all the molecules is

[F = sum frac{m}{L *  v_{x}^{2}}]

[F = frac{m}{L * sum v_{x}^{2}}]

[sum v_{x}^{2} = sum v_{y}^{2} = sum v_{z}^{2} (symmetry)]

= [frac{1}{3}sum V^{2}]

Therefore,  [ F = frac{m}{L*frac{1}{3N}sum V^{2}}]

Now, the pressure is the force per unit area hence,

[P = frac{F}{L^{2}}]

[frac{m}{L^{3}(frac{1}{3N})sum V^{2}}]

[P = frac{3rho }{v^{2}}]

Here, M=total mass of the gas

And ρ=density of the gas

Now, [frac{sum v^{2}}{N}] is written as [{v^{2}}] and is called mean square speed.

[P = frac{3rho }{v^{2}}]

So, this is what the pressure exerted by gas.

In subjects like Physics, there is a proton-to-electron mass ratio represented by symbol ‘μ’ or ‘β’. It is simply said to be the rest mass of the proton that is a baryon found in atoms so it can be divided by that of the electron so a lepton found in atoms. As this is a ratio which is of like-dimensioned physical quantities, i.e., it is a dimensionless quantity which is a function of the dimensionless physical constants and generally has numerical value independent of the system of units, as:

μ = mp/me = 1836.15267343(11).

Mass of One Proton

Every nucleus of a given chemical element has the same number of protons. We can see that this number is generally defined as the atomic number of an element and determines the position of the element in the periodic table. When the number of protons and in a nucleus that generally equals the number of electrons orbiting the nucleus the atom is electrically neutral. So the discovery of the proton dates to the earliest investigations of atomic structure. 

Atomic Mass of Proton

In 1886, Goldstein found that the charge to mass ratio of the positive particles depends totally on the nature of the gas which is present in the discharge tube. So this means that the charge which is the mass ratio denoted by e/m was different for different gases.

So he observed that the charge which is the mass ratio of the positive rays which was highest in case of the gas hydrogen was used in the discharge tube. This is mainly because it is because hydrogen is the lightest atom so m will be the least hence the e/m is the ratio which will be highest in this case.

The particle in the positive rays and along with that in the discharge tube was named a proton. A proton can be said to be produced when we remove an electron that was from the hydrogen atom.

So we see that H (hydrogen atom) → H+   (proton) +   e– (electron)

Significance of Proton Mass

The symbol that is μ is an important fundamental physical constant we can say that because:

• There is nearly all of the science that generally deals with baryonic matter and how the fundamental interactions affect such matter. There is a baryonic matter which generally consists of quarks and particles that is made from quarks – like protons and neutrons. Free neutrons have a half-life of 613.9 seconds. Electrons and protons generally appear to be stable so we can say that to the best of current knowledge. Proton decay theories predict that the proton has a half-life on the order of at least 1032 years. To date, there is no experimental evidence of proton decay.

• As they are stable components of all normal atoms and determine their chemical properties so the proton is the most important baryon while the electron is the most important lepton.

• The symbol μ and the fine structure generally constant denoted by α are the two dimensionless quantities which are emerging in elementary physics and two of the three dimensions are like quantities discussed in Barrow that is 2002.

The proton mass that is denoted by mp is composed primarily of gluons and the quarks that are the up quark and down quark making up the proton. So hence mp and therefore the ratio μ are said to be easily measurable consequences which are of the strong force. So, in fact, it is  in the chiral limit mp which is proportional to the QCD energy scale that is denoted by  ΛQCD. 

Radio waves are the waves that are a sort of electromagnetic radiation and have a recurrence with the longest frequency of radio waves from high 300 GHz to low as 3 kHz; however, someplace it is characterized as over 3 GHz as microwaves. At 300 GHz, the frequency of radio waves is 1 mm, and at 3 kHz is 100 km. They travel at the speed of light simply like all other electromagnetic speeds of radio waves do. Astronomical objects make all the waves that have normally happened. Falsely shaped radio waves are utilized in radio correspondence, radar, computer systems, broadcasting, diverse route frameworks, and various applications of radio waves.

An Introduction to Radio Waves

Radio waves are a kind of electromagnetic wave whose wavelength falls in the electromagnetic spectrum. The radio waves have the longest wavelengths among electromagnetic waves. As like all other electromagnetic waves the radio waves also travel at the speed of light. Radio waves are usually generated by charged particles while accelerating. 

Radio waves are generated artificially by transmitters and received by the antennas or radio receivers. Radio waves are usually used for fixed or mobile radio communication, broadcasting, radar, communication satellites.

Discovery

The radio wave’s concept was first predicted by James Maxwell by predicting the behavior of electromagnetic waves from the Maxwell equation. The concept was later demonstrated by Heinrich Hertz. But the first-ever successful practical implementation was created by Guglielmo Marconi for which he was awarded the Nobel prize. The radio waves were used commercially for the first time in 1900 which was called Hertzian waves and later renamed as Radio waves.

There are two types of radio waves. Long waves can go around obstacles and propagate long ranges like mountains and follow the earth’s contours. Since the ground is not a perfect conductor the signal gets annulated as they follow the earth’s surface. The shorter waves get reflected from Earth’s ionosphere and travel in a straight line and usually have a range of visible horizons. The short waves are called sky waves and the long waves are called the ground waves.

All the objects in space emit some amount of radio waves. The sun constantly emits radio waves which can be captured by Radio telescopes installed in space. These help us in planning the solar flare which may cause disruption in our communication network.

All the communications we use on earth are part of Radio waves from the mobile network to old Radio channels, from Tv to military communications. 

In space, the radio waves travel at the speed of light. But in the material medium, the speed of the Radio waves obeys the inverse square law. The main issue with the propagation of radio waves is diffraction and deflection. With the increase in the length of propagation, the loss due to transmission becomes huge and the signal might suffer data loss. To overcome this issue the concept of relay transmission is used. The relay transmission sites are also called the amplifier which receives the signal, amplifies it, and re-transmits it to the atmosphere.

Radio Waves Definition

Radio waves are typically created by radio transmitters and can be gotten by radio recipients. Radio waves having various frequencies contain different qualities of propagation in the Earth’s environment. The long waves get diffracted around various impediments and follow the outline though the short waves reflect the ionosphere and get back into the great beyond of sky waves.

Frequency Range of Radio Waves

Types of Radio Waves

ELF radio waves, the least of every frequency of radio waves, have a long-range and are valuable in entering water and rock for correspondence with submarines and inside mines and caves. The most remarkable common wellspring of ELF/VLF waves is lightning. LF and MF radio groups incorporate marine and aviation radio, just as commercial AM radio.AM radio recurrence groups fall between 535 kilohertz to 1.7 megahertz. AM radio has a long-range, especially around night.

HF, VHF, and UHF are the radio waves use FM radio, communicate TV sound, public radio service, cellphones, and GPS. These groups regularly use “frequency modulation” (FM) to encode, or dazzle, a sound, or information signal onto the transporter wave.

FM brings about excellent sign quality over AM because ecological components don’t influence the recurrence of how they influence adequacy. The recipient ignores varieties in amplitude.

Short radio waves use frequencies in the HF band, from about 1.7 megahertz to 30 megahertz. Inside that extend, the shortwave range is isolated into a few fragments, some of which are devoted to ordinary telecom stations.

SHF and EHF speak to the most elevated frequencies in the radio band and are some of the time viewed as a feature of the microwave band. Molecules noticeable all around will, in general, assimilate these frequencies, which restrains their range and applications.

Radio Waves Uses

Radio waves uses are explained in correspondence than other electromagnetic waves primarily in light of their attractive proliferation properties, coming from their enormous radio waves wavelength. Radio waves wavelength can go through the atmosphere, foliage, and most structure materials, and by diffraction can twist around blocks, and not at all like other electromagnetic waves, they will, in general, be dissipated instead of consumed by objects bigger than their frequency of radio waves. Radio waves use are found in standard communicate radio and TV, shortwave radio, route and airport regulation, cell communication, and even remote-controlled toys.

Solved Questions

1. What is The Speed of Radio Waves?

In free space (vacuum), the speed of radio waves is the quickest, the “speed of light.” how quick radio waves wavelength travel is that it depends what they are traveling through, most extreme for space, slower for matter contingent upon the kind of matter and the recurrence of the waves.

Fun Facts

1. Clerk Maxwell in the 1860s, initially anticipated that radio waves existed. His hypothesis is called Maxwell’s hypothesis, portraying radio, and light waves.

2. Heinrich Hertz exhibited radio waves in his lab in 1887. A Hertz is a radio wave unit of estimation, as is named after Heinrich Hertz.

3. During the 1890s, Guglielmo Marconi made the main reasonable and usable radio transmitter and beneficiary

Reflection of Light

Reflection is one of the distinctive properties of light. It is the reflection of light, which enables us to see anything. Light reflection occurs when a ray of light meets a smooth polished surface and reflects back. The incident light ray is said to be reflected off the surface when it lands on it. The beam that rebounds is known as the reflected ray. back. Normal is the name given to a perpendicular drawn on a reflective surface. The reflection of an incident beam on a plane mirror is seen in the diagram below.

 

Reflection: The rebound of rays of light from an elegant and glossy surface is called reflection or reflection of light. It is related to a football bouncing back after colliding with a wall or any hard surface.

 

 

What is a Mirror, Exactly?

When you look in the mirror, you see a wonderful, clear image of yourself. It’s not like your reflection in a gleaming automobile. And the vast majority of surfaces encountered in daily life aren’t at all reflecting. At the kitchen table, you don’t see your reflection at all. That’s because, while the table appears to be smooth, it isn’t. Most surfaces would reveal a panorama of peaks and valleys if examined under a microscope.

 

Various Types of Mirrors

The following are the most commonly used mirror types:

In the images formed by a plane mirror, the reflected images are reversed from left to right in their normal proportions. These are the mirrors that are utilised the most.

 

These are spherical mirrors bent outwards that provide a virtual, reduced, and erect image of a real thing.

 

These are inwardly curved spherical mirrors, and the picture they produce is depending on the position of the object.

 

Spherical Mirrors vs Plane Mirrors

• A flat surface is referred to as a plane. A plane mirror is just a mirror with a fully flat, smooth surface. This prevents the image from becoming distorted. A fun-house mirror, on the other hand, maybe the polar opposite, with its different bends and curves making the image look silly.

• A sphere is a 3D replica of a perfect circle, with a constant radius and a consistent curve all the way around. So a spherical mirror is a sphere-shaped mirror with a continuous curve and constant radius of curvature.

• Spherical mirrors can be convex or concave depending on which side the mirrored surface is placed on. A convex mirror is a spherical mirror that has its reflecting surface on the outside of the spherical curve. On the other hand, a concave mirror is a spherical mirror with a mirrored surface on the inside of the curve.

• Virtual, upright representations the same size as the object are created by plane mirrors. By the way, virtual simply implies that the picture is produced behind the mirror rather than in front of it.

Laws of Reflection of Light

• The angle of reflection and incidence are equal.

• The incident ray, reflected ray and normal  point of reflection lies in the same plane.

The angle of incidence is denoted by ‘i’ and angle of reflection is denoted by ‘r’.  The rule of reflection is valid to all types of reflecting surface.

Mirror and Reflection of Light

The mirror is a shiny polished object (glass) which reflects most of the rays of light falling upon it. One side of the mirror is cleaned with an appropriate material to make the opposite side reflective.

Types of Image Formed by Mirrors

• Real Image: Picture which is framed before the mirror and it very well may be acquired on a screen is called a genuine picture.

• Virtual Image: Picture which is framed before the mirror and it very well may be acquired on a screen is called a genuine picture.

Types of Mirror:

Plain Mirror: A mirror having a level surface is known as a plane mirror.

Formation of an image in the plane mirror:

 

• A plane mirror dependably frames a virtual and erect picture.

• The separation of the picture and that of an item is equivalent from the mirror.

• The picture shaped by a plane mirror is horizontally modified.

Spherical Mirror

Mirrors having a curved reflecting surface are called round mirrors. A plane mirror constantly outlines a virtual and erect picture. 

Kinds of Spherical Mirror

• Concave Mirror: Spherical mirror with a reflecting surface bent inwards is known as a concave mirror.

• Convex Mirror: Spherical mirror with a reflecting surface bent outwards is known as a convex mirror.

Important terms in the case of a spherical mirror

• Pole: The focal point of reflecting surface of a round mirror is known as Pole. Pole lies on the outside of the round mirror. It is commonly known by ‘P’. 

• Centre of Curvature: The focal point of a circle; of which the reflecting surface of a round mirror is a section; is known as the center of curvature of the spherical mirror. Centre of curvature is not an element of a spherical mirror. Centre of curvature is  indicated  by the letter ‘C’.

On account of the concave mirror the center of curvature lies before the reflecting surface. Then again, the center of curvature lies behind the reflecting surface on account of a convex mirror.

• The Radius of Curvature: The radius of the circle; of which the reflecting surface of a circular mirror is a section; is known as the Radius of Curvature of the round mirror. The range of curvature of a spherical mirror is signified by letter ‘R’.  Like the center of curvature, the radius of shape lies before the concave mirror and lies behind the convex mirror and isn’t a piece of the mirror as it lies outside the mirror.

• Aperture: The diameter across from the reflecting surface of a round mirror is called aperture.

• Principal Axis: Imaginary line going through th
  e center of curvature and pole of a round mirror are known as the Principal Axis.

• Focus or Principal Focus:  The point on a principal axis which parallel rays; originating from infinity; meet after reflection is known as the Focus or Principal Focus of the round mirror. It is signified by letter “F” 

  

In a concave mirror, similar rays; coming from infinity; converge after reflection at the front of the mirror. Thus, the center point lies in front of a concave mirror.

In a convex mirror, equivalent rays; coming from infinity; emerge to be diverging from the rear mirror. Thus, the focal point  lies at the rear of the convex mirror.

Focal length: The space from pole to focus is called focal length. Focal length is indicated  by the letter ‘f’. Focal length is equivalent to half of the radius of curvature.

Mathematically, we write:

 

[ f = frac{R}{2} ]

 

or

 

[R = 2f ]

Reflection From a Spherical Mirror:

A spherical mirror is a type of mirror in which the reflecting surface is one of the parts of a hollow sphere of glass. Spherical mirrors are further subdivided into two types: 

1. Concave mirror: In a concave mirror the reflection of light is noticed at the bent surface or in other words at the concave surface. We can consider the inner polished surface of the regular spoon as an example for a concave spherical mirror. 

2. Convex mirror: In a convex mirror the reflection of light is observed at the bulging-out surface or in simple terms at the convex surface. The outer polished surface of a regular spoon can be considered as an example for convex mirrors.

Reflection of Rays parallel to Principal Axis

In the case of a concave mirror: A Ray equivalent to the principal axis passes during the principal focus after reflection from a concave mirror.

In the same way, all equivalent rays to the principal axis pass through the principal focus after reflection from a concave mirror. Because a concave mirror converges the similar rays after reflection, thus a concave mirror is also known as a converging mirror.

In the Case of a Convex mirror: A  ray parallel to the principal axis appears to move away from the principal focus after reflecting from the surface of a convex mirror

Likewise, all rays similar to the principal axis of a convex mirror appear to move away or come from principal focus after reflection from a convex mirror. Since a convex mirror diverges the similar rays after reflection, thus it is also known as a diverging mirror. 

Reflection of a Ray Passing Through the Principal Focus

In the Case of the Concave Mirror: Ray going through the principal focus goes parallel to the principal axis after the appearance on account of the concave mirror. 

In the Case of the Convex Mirror: A ray guided towards principal focus goes parallel to the principal axis after reflecting from the outside of a convex mirror.

 

Ray passing through the Centre of Curvature:

In the Case of the Concave Mirror: Beam going through the center of curvature returns at a similar way subsequent to reflecting from the outside of an inward mirror.

In the Case of the Convex Mirror: Beam seems to go through or coordinated towards the center of curvature parallel to the principal axis after reflecting from the surface of a convex mirror.

Ray Incident Obliquely to the Principal Axis: Ray on a slope to the principal axis goes indirectly after reflecting from the pole of both concave and convex mirror and in the same direction.

Image Formation by Concave Mirror

The arrangement of the image relies upon the place of the object. In the case of the concave mirror, there are six possibilities on which position of the object is placed.

a. Object at infinity

b. The object between infinity and the center of curvature (C)

c. An object at the center of curvature (C)

d. The object between the center of curvature (C) and Principal focus (F)

e. An object at Principal Focus (F)

f. Object among Principal Focus (F) and Pole (P)

An Object at Infinity

Since parallel rays coming from the object converge at the principal focus, F of a concave mirror; after reflection. Hence, when the object is at infinity the image will form at F.

 

Properties of the image

• Point sized

• Highly diminished

• Real and inverted

The Object Between Infinity and Centre of Curvature

When the object is positioned between infinity and center of curvature of a concave mirror the image is created between the center of curvature (C) and focus (F).

Properties of the image

An Object at the Centre of Curvature (C)

When the object is located at the center of curvature (C) of a concave mirror, a real and inverted image is created at a similar position.

Properties of the image

• Same size as the object

• Real and inverted

Object Among Centre of Curvature (C) and Principal Focus (F)

When the object is to be found between the center of curvature and the principal focus of a concave mirror, a real image is created beyond the center of curvature (C). 

Properties of the image

• Larger than object

• Real and inverted

An Object at Principal Focus (F):

When the point is located at the principal focus (F) of a concave mirror, a highly inflated image is created at infinity.

Properties of the image:

• Highly enlarged

• Real and inverted

The Object Between Principal Focus (F) and Pole (P):

When the point is located between principal focus and pole of a concave mirror, an inflamed, virtual and erect image is created behind the mirror.

Properties of the image:

• Enlarged

• Virtual and erect

Image Formation by Convex Mirror

< p>Two possibilities only are possible of the position of the object in the case of a convex mirror, i.e. the object at infinity and object among infinity and pole of a convex mirror.

An Object at Infinity: When the object is at the infinity, a point-sized image is formed at principal focus behind the convex mirror. 

Properties of image: Image is extremely diminished, virtual and erect.

The Object Between Infinity and Pole: When the object is among infinity and pole of a convex mirror, a diminished, virtual and erect image is created among pole and focus behind the mirror.

Characteristics of Object: object is diminished, virtual and erect.

Frequency is recognized as the fundamental characteristic of a wave. The definition of frequency is defined as the calculation (measurement) of the sum of waves that are passing through one point in a unit of time.

We also know what velocity is. In short, it is the rate of change of displacement. We need a brief explanation to state the term ‘velocity’—the total distance covered by a point. Within the same wave is called the velocity of the wave.

Here is the relation between velocity and frequency:

V = f × λ 

Here, 

V = velocity of the wave measure (using m/s).

f = frequency of the wave measured (using Hz).

λ = wavelength of the wave measured (using m).

Explanation on Relation Between Frequency Wavelength and Velocity

Do you know the characteristics of a wave? Wavelength, amplitude, frequency, and velocity- these four parameters are the characteristics. If a wave has a constant wavelength, you may notice the increment of velocity as well as frequency. 

These three parameters are interdependent. Scientists have published many theorems and formulas based on the relation between wavelength frequency and velocity in particle physics.

Let’s consider some examples which are related to the relation between frequency and wavelength and velocity:

1. When a particle is radiating a wave of constant wavelength, and the value of frequency is doubled, the radiated wave’s velocity is also doubled .

2. When you notice a wave having a constant wavelength, and its frequency is four times its wavelength, then the velocity you observe is increased by four times.

Relation Between Speed and Frequency

Frequency is the total number of occurrences of a wave traveled in space (or vacuum) per unit of time. The unit for frequency is Hertz (Hz). Some common symbols are associated with frequency such as V and f.

The SI unit is Hz. S^-1 is the SI base unit. The dimension for frequency is T¹. The measurement of frequency is the total occurrences obtained due to a repeating wave per second. 

The more is the period in the duration of time; the less will be the occurrences. Hence, occurrences and frequency both are reciprocal to each other.

To rectify any kind of oscillatory and vibratory phenomena, physicists use frequency at most. They use frequency to determine the calculation of mechanical vibrations, sound (audio signals), light, and radio waves. 

Relationship Between Amplitude and Frequency

Although there is no direct relationship between frequency and amplitude or vice versa. Individually, they can be expressed by rearranging the terms of the wave equation.

Amplitude to Frequency Formula

The wave equation can be rearranged to express amplitude in terms of frequency and other variables.

[A = y (t) sin (2pi ft + phi) ]

Frequency to Amplitude Formula

The wave equation can be rearranged to describe frequency in terms of amplitude and other variables.

[f = sin – 1(y(t)A) – phi 2 pi t ]

Finding the Relation Between Frequency and Time

The number of cycles per unit time – the statement is used to define many cyclical processes. Those cyclical processes are waves, oscillation, frequency, and rotation, and so on. In particle physics, many physicists apply these terms to calculate certain values.

The relation between frequency and time is helping them quite enough to determine many requisite values for the benefits. Also, you will learn about frequency in optics, acoustics, and radio chapters from physics.

Frequency is denoted by a symbol (obtained from Latin letter) i.e. f

The relation between frequency and time is equal to f = 1/T

Before the invention of unit Hertz, physicists used the unit of cycles per second (cps) for frequency. This is a traditional unit of measurement. Engineers tried to calculate the frequency using certain mechanical devices. 

Statistics Between Frequency and Period

Slower or longer waves are explained with the term ‘wave period’ (not frequency). Such waves are ocean surface waves. But waves like audio radio and light are expressed with the term ‘frequency’. These waves are faster and possess higher periods.

The table given below will show you the conversion of frequency to the period:

Mathematical Example: The sound produced by an object in the air has a wavelength of 20 cm. Find the object’s frequency and period if the sound velocity in the air is 340 ms^-1.

In this, Wave-length, γ = 20 cm = 0.2 m

Sound-velocity = 340 ms^-1

Frequency, f =?

Period (time), T = ?

We know Velocity = fγ

So, f = v/γ = 340 ms^-1 / 0.20 m = 1700 Hz

And T = 1/f = 1 / 1700 s^-1

= 0.000588 s 

= 5.88 x 10^-4 s

Conclusion

Thank you for reading this a
rticle. We hope this article on Velocity and frequency was helpful for the students. You can also access sample papers, previous year papers, revision notes, and important questions from the website.

The mechanical property of a material to withstand the compression or the elongation concerning its length is called Young’s Modulus which is also referred to as the Elastic Modulus or Tensile Modulus is denoted as E or Y.

Young’s Modulus measures the mechanical properties of linear elastic solids such as rods and wires. Other numbers give us a measure of elastic properties of a material, such as the Bulk modulus and shear modulus, but the value of Young’s Modulus is most commonly used in the world. Young’s Modulus is used very generally because it gives us information about the tensile elasticity of a material which is the ability to deform along an axis.
 

Young’s modulus describes the relationship between stress, i.e. force per unit area and strain, i.e. proportional deformation in an object. The Young’s modulus is named after Thomas Young who was a British scientist. Any solid object will deform when a particular load is applied to it. But if the object is elastic, then the body regains into its original shape when the pressure is removed from the object. Many materials are not linear elastic beyond a small amount of deformation and Young’s modulus applies only to linear elastic substances.

Young’s Modulus Formula is E = [frac {sigma} {varepsilon}]

Young’s Modulus Formula From Other Quantities: 

 

E = [frac {FL_0} {ADelta L}]

Notations That Are Used in the Young’s Modulus Formula are as Follows:

• E is Young’s modulus in Pa

• σ is uniaxial stress in Pa

• ε is a strain or proportional deformation

• F is the force exerted by the object under tension

• A is the actual cross-sectional area

• ΔL is a change in length

• L0 is the actual length
  

Units and Dimension of Young’s Modulus Formula

• SI unit- Pa

• Imperial Unit- PSI

• Dimension- ML^-1T^-2
  

With the value of Young’s modulus for a material, we can find the rigidity of the body. This is only because it tells us about the ability of the body to be able to resist deformation on the application of force.

The Young’s Modulus values ( x 10⁹ N/m²)
 

 of different material are given:

Tensile Stress and Tensile Strength in Young’s Modulus:

Tensile stress is the force that causes an object to stretch. Ductile materials can bear higher tensile stress, and brittle materials can not withstand higher tensile stress as they break away easily. Elastic modulus is a tensile stress property, and it is the ratio of stress and strain when the change in the object is completely elastic. Fracture stress is another property of tensile stress. On the other hand, tensile strength is the maximum force an object can withstand before breaking or tearing down. When the stress is less than the tensile strength of an object, it expands initially and returns back to its normal shape and size once the force is removed but, if the stress exceeds the tensile strength of an object, it starts tearing down. 

Young’s modulus is expressed as the ratio of tensile stress and tensile strain. Here, tensile strain is the damage caused by a force when it tries to expand an object. Young’s modulus is very important to judge the strength of an object, and the highest young modulus can be seen in diamond. Objects that are flexible generally have low Young’s modulus as they can easily change their volume when they are subjected to external force or pressure. 

So, we can conclude that objects with high Young’s modulus are very inelastic and could not be stretched but the objects with less Young’s modulus value are very elastic and easily alter when they are subjected to external force or pressure. This principle is very useful in deciding the construction material to be used. For example, the builders use concrete, which has a high modulus value, to build bridges and roads as they are subjected to heavy weights every day. Similarly, steel is chosen to build railways as the steel has a high modulus value to withstand the heavyweight of the train.

What is a Bulk Modulus?

The bulk modulus is defined as the proportion of the volumetric stress related to the volumetric strain of specified material, while the material deformation is within the elastic limit. In more simple words, we can say that the bulk modulus is nothing but a numerical constant used to measure and describe the elastic properties of a solid or fluid when a particular pressure is applied on all the surfaces.

The bulk modulus of elasticity is one of the measures of the mechanical properties of solids and whereas the other elastic modules include Young’s modulus and the Shear modulus. The bulk elastic properties of a material are always used to determine how much the material will compress under a given amount of external pressure. Here it is very crucial to find and also to note the ratio of the change in pressure to the fractional volume of compression.
 

The value is denoted with the symbol ‘K’, and it has the dimension of force per unit area. It is expressed in the units per square inch, i.e. psi in the English system and newtons per square meter (N/m²) in the metric system.

Relation Between Elastic Constants 

The Young’s modulus, the bulk modulus as well as the Rigidity modulus of an elastic solid are together called the Elastic constants. When a deforming force is acting on a solid, it will result in a change in its original dimension. In such cases, we can use the relation between the elastic constants to understand the magnitude of the deformation.

Elastic Constant Formula

Where K is the Bulk modulus, G is the shear modulus or modulus of rigidity, and E is Young’s modulus or modulus of Elasticity.

 

Individually, Young’s modulus and bulk modulus, as well as the modulus of rigidity, are related as follows-

• The formula for the relation between modulus of elasticity and modulus of rigidity is  E = 2G(1 + μ), and the SI unit is N/m² or pascal(Pa)

• The formula for the relation between Young’s modulus and bulk modulus is E = 3K(1 − 2μ), and the SI unit is N/m² or pascal(Pa)
  

Relation Between Bulk Modulus and Young’s Modulus

The Young’s Modulus is the ability of any material to resist the change along its length whereas the Bulk Modulus is the ability of any material to resist the change in its volume. The bulk modulus and young’s modulus relation can be mathematically expressed as;

 

Young’s Modulus And Bulk Modulus Relation

 

K= [frac {Y}{3}]

 

1−(2/μ)

Where K is the Bulk modulus, Y is Young’s modulus, and μ is the Poisson’s ratio.

 

For more information related to previous year question papers, important questions, model papers, syllabus, exam pattern, reference material, free textbook PDFs and other information related to general and competitive exams, keep visiting . Students can now access our resources from ‘s mobile app.