Magic With Physics

Gravitational Force

2020-05-23T18:59:00.008+05:30

Newton's Law Of Gravitation:
Newton's Law of gravitation states that,"Every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

F ∝ M m
F ∝ 1/r²
∴ F ∝ M m/r²
∴ F = G M m/r²
G is a universal gravitational constant

SI Unit of universal gravitational constant is Nm²/kg².
And the C. G. S. unit is dynecm²/g²

Value Of G is 6.673×10^-11

And the dimension of G is

Points to study in Gravitational Force
👉 Acceleration due to gravity (g)

👉 Variation of 'g' due to Altitude, Latitude and Depth

👉 Study of Satellite
1) Projection of satellite
2) Periodic time of satellite
3) Binding energy and Escape velocity of satellite.
👉 Kepler's law of motion

👉 Weightlessness.

👉 Uses of satellite.

👉 About Planets

👉 Black Hole

👉 Acceleration due to gravity (g)

Let M is mass of the earth, R is radius of the earth. Consider an object of mass m situated on the surface of the earth, g is the gravitational acceleration due to gravity at the earth's surface. The weight of the object is equal to gravitational Force acting on it.

On earth surface,

Weight of the object = Gravitational force

mg = GMm/R²

g = GM /R²

At height h,

gh = GM /(R+h)²

or gh = g (R/R+h)²

👉 Variation of 'g' due to Altitude, Latitude and Depth

(1) Variation of g due to Altitude

gh = g [1-2h/R]

(2) Variation of g due to Depth

gd = g [1-d/R]

(3) Variation of g due to Latitude

g' = g - R⍵²θ²

Variation of g due to latitude at sea level

Latitude	g (m/s²)
0⁰	9.7804
10⁰	9.7819
20⁰	9.7864
30⁰	9.7933
40⁰	9.8017
50⁰	9.8107
60⁰	9.8192
70⁰	9.8261
80⁰	9.8306
90⁰	9.8322

👉Study of Satellite

Projection of satellite

Satellite means an object which revolves in an orbit around a planet. There is many artificial satellite which is man made & Moon is the natural satellite of the Earth.

For projection of satellite there is minimum two stage rocket is used. In this rocket satellite is kept at the tip means at the top position. Initially the fuel in the first stage of the rocket is ignited on earth surface , so the rocket riser to desired height. Now by remote control, the empty first stage is detached from rocket and rocket rotates 90 degree so that it points in horizontal direction. When fuel in second stage is completely burn then second stage is detached. The resulting motion of the satellite depends upon the velocity of the projection given to it.

" Critical Velocity, the minimum horizontal velocity of projection that must be given to a satellite at a certain height, so it can revolve in a circular orbit around earth.

" Escape Velocity, the minimum velocity with which a body should be projected from the surface of the earth, so that it escape from the earth's gravitational field.

Different cases of projection of satellite

Satellite moves in elliptical orbit, when the velocity of the projection is less than the critical velocity. But the point of projection is apogee and in the orbit the satellite comes closer to the earth with its perigee point lying at 180 degree. If it enters the atmosphere while coming towards perigee it will loose energy and spiral down. If does not enter the atmosphere, it will continue to move in elliptical orbit.

Elliptical orbit when Vc<V<Ve

If the velocity of projection is greater than the critical velocity but less than the escape velocity, then the satellite moves in elliptical orbit and its apogee, or point of greatest distance from the earth, will be greater than projection height.

Circular orbit when V = Vc

Satellite moves in circular orbit around the earth when velocity of the projection is equal to the critical velocity.

Parabolic path when V =Ve

Satellite moves in parabolic path when velocity of projection is equal to escape velocity.

Hyperbolic path when V>Ve

Satellite escape from gravitational pull of the earth and travel infinitely when the velocity of projection is greater than the escape velocity and when the orbit is hyperbolic

Periodic time of satellite

The time taken by the satellite to complete one revolution round the earth is called its period or periodic time (T).

👉 Kepler's law of motion

Kepler's first law (Law of orbit)

Every planet revolves in an elliptical orbit round the sun, with the sun situated at one of the focii of the ellipse.

Kepler's second law (Law of areas)

The radius vector drawn from the sun to any planet sweeps out equal areas in equal intervals of time.

i.e. The areal vector of the radius vector is constant.

[ According to the Kepler's second law, when a planet is closest to the rain, its speed is maximum and when it is farthest from the sun its speed is minimum ]

Kepler's third law (Law of period)

The square of the period of revolution of the planet around the sun is directly proportional to the cube of the semi major axis of the elliptical orbit. This law is known as the harmonic law.

Aldehydes , Ketones And Carboxylic Acids

2020-05-20T14:48:00.051+05:30

Welcome to Organic Chemistry Class. In this post we discuss the organic chemistry chapter Aldehydes, Kitones and Carboxylic Acids.

Aldehyde & Ketone are also known as Carbonyl Compound because present of (>C=O) Carbonyl group.

What Is An Aldehyde ?

An Aldehyde is the first oxidation product of primary alcohol. The functional group is formyl or aldehyde group (-CHO )always present at the terminal carbon of the chain.

What Is Ketone ?

A Kitone is the first oxidation product of secondary alcohol. The functional group is keto or oxo group ( >C=O ) not located at the terminal carbon of the chain.

What Is Carbonyl Group ?

Carbonyl Group is a functional group in which a carbon atom is attached to an Oxygen atom by a double bond and remaining two valencies of carbon atom are free is called a carbonyl group and represent as >C=O

Nomenclature of Aldehydes:
Common Name System:
(1) The names of aldehydes are derived from the common names of acids.
(2) THe suffix ' -ic acid ' of an acid replace by 'aldehyde'.
(3) The positions of the substituents in the molecule are indicated by Greek letters α,β,y, etc. starting from the carbon atom attached to the carbonyl group

IUPAC System:
(1) The longest carbon atoms chain containing aldehyde carbon atom is selected as a parent hydrocarbon.
(2) 'e' of the alkane is replaced by 'al'.
(3) the position of aldehyde group need not be mentioned since it is a;ways at the end position.
(4) The substituent in the alkyl group are prefixed in an alphabetical order by appropriate locants.

Compound	Common name	IUPAC name
HCHO	Formaldehyde	Methanal
CH3CHO	Acetaldehyde	Ethanal

Nomenclature of Ketones:
Common Name System:
(1) Ketones are name according to the alkyl groups attached to the carbonyl carbon atom followed by the word ketone
(2) The substituents in the alkyl groups are indicated by Greek lettters α,β,y, etc. starting from the carbon atom attached to the carbonyl group.

IUPAC System:
(1) The longest continuous chain containing carbonyl carbon atom is selected as a parent hydrocarbon.
(2) 'e' of the alkane is replaced by 'one'.
(3) The position of carbonyl group is represented by the lowest locant.
(4) The substituents in the alkyl groups are prefixed in the alphabetical order along with their positions by appropriate locants.

Compound	Common name	IUPAC name
H3C. COCH3	dimethyl ketone (acetone)	Propanone
H3C. COC2H5	ethyl methyl ketone	butanone

Preparation Methods Of Aldehyde And Ketone

Aldehyde and Ketone can be prepared by following methods:

Oxidation of alcohol
Catalytic dehydrogenation of alcohols
Oxidation of alkenes
Hydration of alkenes
Hydrolysis of geminal dihalide
Pyrolysis of calcium salt of carboxylic acid
Reduction of acid chloride
Oxo process
Wacker process

Oxidation of alcohol :

Aldehyde and ketone can be prepared by controlled oxidation of 1° & 2° alcohol using acidified solution of potassium permanganate KMnO₄ or potassium dichromate K2Cr2O7 . 1° alcohol produce Aldehyde and 2° alcohol produce Ketone.

2. Catalytic dehydrogenation of alcohols :

When Aldehyde and Ketone can be prepared, when vapor of 1° and 2° alcohol is pass over copper catalyst at 300°C result in the formation of aldehyde and ketone.

3. Oxidation of alkenes : ( ozonolysis )

When alkene subjected for oxidation with ozone gas and on hydrolysis with zinc dust it gives aldehyde and ketone.

4. Hydration of alkenes :

when alkene such as Acetylene on hydrogen yield. water molecule is added to acetylene in the presence of mercuric sulphate HgSO4 and sulfuric acid, it result in the formation of unstable molecule called as enol. which is on entra molecule rearrangement gives acetaldehyde.

Hydrogen of alkene other then acetylene gives Ketone. water is added according to marconi rule to form unstable enol, which is on rearrangement gives Ketone.

5. hydrolysis of geminal dihalide :

Geminal dihalide are compound which has two halogen attached to same carbon. Ketone, Aldehyde can be prepare by alkene hydrolysis of geminal dihalide in which two halogen atom can be replace with OH group. result in the formation of unstable diol. which is hydration result in the formation of wither Aldehyde or Ketone.

6. Pyrolysis of calcium salt of carboxylic acid :

Symmetrical ketone can be prepare by this method, when calcium salt of carboxylic acid is heated at 400°C. we only can prepare ketone by this method and can not prepare aldehyde.

7. Reduction of acid chloride :

Aldehyde can be prepare by hydrogenation of acid chloride in presence of platinum supported over barium sulfate solution

What is Schiff's reagent ?

Schiff's reagent is an oxidizing agent. Schiff's reagent is prepared by dissolving pink p-rosaniline hydrochloride in water and passing SO2 gas till the pink solution is decolourised.

When an Aldehyde is added to Schiff's reagent, the colourless solution turns pink or in magenta colour and aldehyde is oxidised to a carboxylic acid.

Did u know 🤔🤔

Formaldehyde is gas at room temperature.
Formaldehyde is used as a disinfectant.
Formaldehyde is use for silvering mirrors.
Formaldehyde is use in the preparation of variety of plastics and resins.
Acetaldehyde boils at 20 °C
Acetaldehyde is used as a starting material for the preparation of many compounds.
Acetone is used as a commercial solvent.
Acetone is used in manufacture of explosives, lacquers, paint removers, plastic, drugs, perfumes,etc.
density of aldehyde & ketone is less than water.

Physics Intro-SI Prefixes, units, Dimensions, symbols etc

2020-05-08T09:29:00.019+05:30

Physical Quantity

All the quantities in terms of which laws of physics are described and which can be measured directly or indirectly are called physical quantities.

For example mass, length, speed, time etc.

Types of Physics Quantity

1) Fundamental Qualntities

The physical quantities which do not depend upon other physical quantities are called fundamental quantities or also known as base physical quantities

e.g. Time, temperature, mass, length, electric current, luminous intensity

and amount of substance

2) Derived quantities

The physical quantities which depend on

Fundamental quantities are called. Derived quantities

e.g. Acceleration, speed, force etc.

Unit

The chosen standerd of measurement of a physical quantity, which has the same nature as that of the quantity is called the unit of that quantity.

Choice of Unit

The first thing is that it should have international acceptation that means Universally accepted and also accurately defined and it should not change with time.

Fundamental and Derived Units

Fundamental units means which are independent of unit of other physical quantity and cannot be further resolve into any other units of the units of fundamental physical quantities are called

Fundamental or base units.

e.g. metre, kilogram, second etc

All unit other than fundamental are Derived units, which are depend on fundamental units.

e.g. unit of speed (metre per sec) (which depend upon length)

Unit of time, unit of momentum etc.

Different types of system of units

C.G.S. units (Centimetre-Gram-Second)
In this system unit of length is centimeter,
mass is gram and for time is second

M.K.S. units (Metre-Kilogram-Second)
In this system unit of length is metre, mass is kilogram and for time is second

S.I. units (international System)
In 1971 CGPM held its meeting and decided a system of units which is known as S.I. (international system) of units. By international agreement, 7 physical quantities have been chosen as fundamental or base physical quantities.

S.No.	Quantity	Name of Units	Symbol
1	Length	metre	m
2	Mass	kilogram	kg
3	Time	second	s
4	Electric Current	ampere	A
5	Termodyanamic Temperature	kelvin	K
6	Amount of Substance	mole	mol
7	Luminous Intensity	candela	cd

S.No.	Supplementary physical quantity	Supplementary unit	Symbol
1	Plane angle	radian	rad
2	Solid angle	steradian	sr

SI Prefixes:

Power of 10	prefix	symbol
18	exa	E
15	peta	P
12	tera	T
9	giga	G
6	maga	M
3	kilo	k
2	hecto	h
1	deka	da
-1	deci	d
-2	centi	c
-3	milli	m
-6	micro	μ
-9	nano	n
-12	pico	p
-15	femto	f
-18	atto	a

Some Important Practical Units :

(a) 1A.U.(Astronomical unit) = 1.496 × 10¹¹m

(b) 1ly (light year) = 9.46 × 10¹⁵ m

(c) 1 parsec = 3.1 × 10¹⁶ m

(d) 1 micron = 10¯⁶ m

(e) 1nanometre = 10¯⁹

(f) 1 angstrom = 10¯¹⁰

(g) 1 C.S.L(chandrasekhar limit) = 1.4 times the mass of the sun

(h) 1 amu = 1.67×10¯²⁷ kg

(i) 1 pound = 453.6 g = 0.4536 kg

(j) 1 bar = 1atm pressure = 10⁵ N/m² = 760. mmHg

Some Important Physical Constant

Velocity of light in vacuum (c) = 3 × 108 ms-1
Velocity of sound in air at STP = 331 ms-1
Acceleration due to gravity (g) = 9.81 ms-2
Avogadro number (N) = 6.023 × 1023/mol
Density of water at 4oC = 1000 kgm-3 or 1 g/cc.
Absolute zero = -273.15oC or 0 K
Atomic mass unit = 1.66 × 10-27 kg
Quantum of charge (e) = 1.602 × 10-19 C
Stefan’s constant = 5.67 × 10–8 W/m2/K4
Boltzmann’s constant (K) = 1.381 × 10-23 JK-1
One atmosphere = 76 cm Hg = 1.013 × 105 Pa
Mechanical equivalent of heat (J) = 4.186 J/cal
Planck’s constant (h) = 6.626 × 10-34 Js
Universal gas constant (R) = 8.314 J/mol–K
Permeability of free space () = 4π × 10-7 Hm-1
Permittivity of free space () = 8.854 × 10-12 Fm-1
The density of air at S.T.P. = 1.293 kg m-3
Universal gravitational constant = 6.67 × 10-11 Nm2kg-2

Astronomical Constant

S. No.	Quantity	Value	Unit
1	Mass of the sun	1.99×10^30	kg
2	Radius of the sun	6.95×10^8	m
3	Mass of the earth	5.98×10^24	kg
4	Mean radius of the earth	6.37×10^6	m
5	Mass of the moon	7.36×10^22	kg
6	Radius of the moon	1.74×10^6	m
7	Mean earth-sun distance	1.50×10^11	m
8	Mean earth-moon distance	3.84×10^8	m
9	Escape speed from the earth	11.2	km/s
10	Escape sore from the moon	2.38	km/s

Unit and Dimension of Physical Quantities

S.No.	Physical Quantity	Symbol	SI Unit	Dimension
1	Displacement	s	Metre (m)	L
2	Mass	m,M	Kilogram	M
3	Time	t	Second (s)	T
4	Area	A	m2	L2
5	Volume	V	m3	L3
6	Density	ρ	kg m–3	ML–3
7	Velocity	v,u	m s–1	LT–1
8	Acceleration	a	m s–2	LT–2
9	Force	F	newton (N)	MLT–2
10	Work	W	joule (J)	ML2T–2
11	Energy	E,U,K	joule (J)	ML2T–2
12	Power	P	watt (W)	ML2T–3
13	Momentum	p	kg-m s–1	MLT–1
14	Gravitational constant	G	N-m2 kg–2	L3M–1T–2
15	Angle	Ө	radian
16	Angular velocity	ω	rad s–1	T–1
17	Angular Acceleration	∝	rad s–2	T–2
18	Angular Momentum	L	kg-m2 s–1	ML2T–1
19	Moment of inertia	I	kg-m2	ML2
20	Torque	τ	N-m	ML2T–2
21	Angular frequency	ω	rad s–1	T–1
22	Frequency	v	hertz (Hz)	T–1
23	Period	T	s	T
24	Young's modulus	Y	N m–2	ML–1T–2
25	Bulk modulus	B	N m–2	ML–1T–2
26	Shear modulus	η	N m–2	MLT–2
27	Surface tension	S	N m–1	MT–2
28	Coefficient of viscosity	η	N-s m–2	ML–1T–1
29	Pressure	P,p	N m–2, Pa	ML–1T–2
30	Wavelength	λ	m	L
31	Intensity of wave	I	W m–2	MT–3
32	Temperature	T	Kelvin (K)
33	Specific heat capacity	c	J kg–1 -K–1	L2T–2K–1
34	Stefan's constant	σ	W m–2 -K–4	MT–3K–4
35	Heat	Q	J	ML2T–2
36	Thermal conductivity	K	W m–1 -K–1	MLT–3K–1
37	Current	I	Ampere (A)	I
38	Charge	q,Q	coulomb (C)	IT
39	Current density	j	A m–2	IL–2
40	Electrical conductivity	σ	1/Ω -m	I2T3M–1L–3
41	Dielectric constant	k
42	Electric dipole moment	p	C-m	LIT
43	Electric field	E	Vm–1	MLI–1T–3
44	Potential	V	volt (V)	ML2I–1T–3
45	Electric flux	Φ	V-m	ML3I–1T–3
46	Capacitance	C	farad (F)	I2T4M–1L–2
47	Electromotive force	E	volt (V)	ML2I–1T–3
48	Resistance	R	ohm (Ω)	ML2I–2T–3
49	Permittivity of space	ε0	C2N–1 -m–2	I2T4M–1L–3
50	Permeability of space	μ0	N A–2	MLI–2T–2
51	Magnetic field	B	tesla (T)	MI–1T–2
52	Magnetic flux	Φ0	weber (Wb)	ML2I–1T–2
53	Magnetic	μ	N-mT–1	IL2
54	Inductance	L	henry (H)	ML2I–2T–2

Force

2020-04-03T22:38:00.015+05:30

When we heard Force, our first thinking about this word is Pull or Push. When you push something you exert a force toward yourself, and when you pull something then you exert force toward yourself.

Not only living body, non-living body also exert force. Such as tension force in a string, if the heavy block is attached to the string and also Normal force perpendicular to the surface if the block placed on any surface.

The SI Unit is newton

Force is vector quantity

We can find resultant force of body if more then one force act on a body by using law of vector addition.

According to the Newton's Third law of motion "If a body A exerts a force F on another body B, then B exerts a -F force on A"

"Every action their is always an equal and opposite reaction."

Their is four categories in which we can place various types of forces
(1) Electromagnetic Force

(2) Gravitational Force

(3) Nuclear

(4) Weak Force

( click on the type of force to study )

FE Vs FG

______________________________________
Gravitational Force

Newton's Law Of Gravitation:
Newton's Law of gravitation states that,"Every particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them."

F ∝ M m
F ∝ 1/r²
∴ F ∝ M m/r²
∴ F = G M m/r²
G is a universal gravitational constant

SI Unit of universal gravitational constant is Nm²/kg².
And the C. G. S. unit is dynecm²/g²

Value Of G is 6.673×10^-11

And the dimension of G is

👉 Acceleration due to gravity (g)

On earth surface,

Weight of the object = Gravitational force

mg = GMm/R²

g = GM /R²

At height h,

gh = GM /(R+h)²

or gh = g (R/R+h)²

👉 Variation of 'g' due to Altitude, Latitude and Depth

(1) Variation of g due to Altitude

gh = g [1-2h/R]

(2) Variation of g due to Depth

gd = g [1-d/R]

(3) Variation of g due to Latitude

g' = g - R⍵²θ²

continue reading

______________________________________
Electromagnetic force

👉 Charge :
Charge is the property associated with matter due to which it produce the experience electrical and magnetic effect.

Current(I) = Charge(Q)/Time(t)
▪ charge is derived quantity

Q = I×t

We know about the Gravitational Force, similarly in the Electromagnetic Force we study the Force which is proportional to the product of their charge and inversely proportional to the square of distance between them.

👉 Coulomb's Law

F = k q₁q₂ /r²

  Where q₁ & q₂ are the charges on the particle and 'r' is the distance between them and 'k' is the constant. The Force is attractive if the charges are opposites signs and is repulsive if they are same signs. We can write Coulumb's Law



Where k

k = 1/4πε₀

Where  ε = 8.85419 × 10^-12 C²/N-m²

And the value of 'k'is

k = 9.0×10^9 N-m²/C²

👉 Distribution of Charge

▪ Linear charge distribution :

Charge per unit lengta

λ = Q/ l

▪Surface charge distribution :

Charge per unit area

σ = Q/A

▪Volumetric charge distribution :

Charge per unit volume

९ = Q/V

👉 Relationships between λ, σ & ९

σ = dQ/dA

= dQ/l.dx

= dλ/dx

  ∴ ९ = dσ/dx



👉 Electric Field :



  The space around an electric charge, where it exerts a force on another charge is an 'electric field'.

E = KQ/r²

Where 'F' is the Force experienced by a small positive test charge q₀ due to charge q.

It's SI unit is NC^-1.   It is a vector quantity. We can add charge is their is more charge responsible for electric field. Then,

✦ Electric Potential Energy :

It is defined as the amount of work done required in carrying an charge slowly either from infinity to a certain point in the electric field or vice-versa

U =q₁q₂/r

✦Electric Potential (V) :

It is defined as the amount of work done required in carrying unit positive charge slowly either from infinity to a certain point in electric field or vive-versa

Physicists And Their Discovery

2020-03-27T22:34:00.006+05:30

Physicists And Their Discovery

Name Of Physicist	Discovery
Abdus Salam	Unification of weak and electromagnetic interactions
Albert Einstein	Explanation of photoelectric effect & Theory of Relativity
Archimedes	Principle of buoyancy & Principle of the lever
Arthur Compton	light can behave as a particle as well as wave
Alessandro Volta	Invented electric battery & Wrote First electromotive series
Alhazen	Explained why camera image are upside down
Amedeo Avogadro	Elements could exist in the form of molecules rather than as individual atom & Originator of Avogadro's law.
Benjamin Frankli	A founder father of USA & gives the electrical term +ve & -ve
C.H. Townes	Invented Maser & Laser and established black hole is center of milky way
Christiaan Huygens	Wave theory of light
C.V. Raman	Raman Effect; Inelastic scattering of light by molecules
Daniel Bernoulli	Bernoulli effect
Edwin Hubble	Expanding Universe
Enrico Fermi	Controlled nuclear Fission
Ernest Orlando Lawrence	Invented Cyclotron
Ernest Rutherford	Father of nuclear chemistry; Nuclear model of atom
Ernest Walton	First high energy particle accelerator
Galileo Galilei	Law of Inertia
Heinrich Rudolf Hertz	Generation of Electromagnetic wave
Hans Christian Oersted	Discovered Electromagnetism
Hideki yukawa	Theory of nuclear force
Homi Jahangir Bhabha	Cascade process of cosmic radiation
Issac Newton	Universal law of gravitation; Laws of motion; Reflecting telescope
Inge Lehmann	Analyzed earthquake waves
John Wallis	Conservation of momentum
James Clark Maxwell	Light is electromagnetic wave
James chadwick	Discovered the Neutron
John Bardeen	Transistor; Theory of super conductivity
J.C. Bose	Ultra short radio wave
J.J. Thomson	Electron
John Michel	Tension balance
Johannes Kepler	Discovered that solar system's planet are in elliptical path
Joseph Henry	Built Electromagnets
Lev Davidovich Landau	Liquid Helium; Theory of condensed matter
Louis Victor de Broglie	Wave nature of matter
Lise Meitner	Invented atomic battery & Discovered nuclear fission
Marie Sklodowska Curie	Discovery of radium and polonium; Studies in natural radioactivity
Michael Faraday	Laws of electromagnetic induction & Faraday's laws of electrolysis
M.N. Saha	Thermal ionisation
Max Plank	Founded quantum theory
Niels Bohr	Quantum Model of Hydrogen atom
Paul Dirac	Relativistic theory of electron; Quantum statistics
Pyotr Kapitsa	Superfluidity
Robert Hook	Discovered Hook's law in physics & Discovered cells
R.A. Millikan	Measurements of electronic charge
S. Chandrashekhar	Chandrashekhar limit &Evolution of stars
S.N. Bose	Quantum statistics
Victor Francis Hess	Cosmic Radiation
Warner Heisenberg	Quantum mechanics; Uncertainty principle
W.K. Roentgen	X-ray
Willard Gibbs	Vector Analysis
William Gilbert	Scientific study of Magnetism
Wolfgang Pauli	Exclusion principle
	Home

Wave

2020-03-26T12:28:00.015+05:30

✦ Wave Motion:

Wave motion is a type of motion in which the disturbance travels from one point of the medium to another but the particles of the medium do not travel form one point to another.

For the propagation of wave, medium must have inertia and elasticity. These two properties of medium decide the speed of wave.

✦Amplitude:

The maximum displacement of any particle from its mean position is called amplitude (a) of the wave.

✦Period:

The time taken (T) for any particle to complete one vibration is called period of the wave.

✦Frequency:

The number of vibrations per second by a particle is called frequency (n) of the waves where

n = 1/T. The frequency can also be said to be the number of waves passing per second across any point of the medium.

✦Wavelength:

The distance between two consecutive particles of the medium which are in the same phase or which differ in phase by 2π (radians) is called wavelength (λ) of the wave.

✦ Types of waves

There are Two types of waves

1) Mechanical wave : These waves require material for their propagation.

For example : Sound waves, etc.

There are two types of Mechanical waves

i) Transverse wave: The particles of medium oscillate in a direction perpendicular to the direction of wave propagation.

ii) Longitudinal waves: The particles of medium oscillate about their mean position along the direction of wave propagation.

2) Non mechanical waves (Electromagnetic wave) : This waves do not require any material medium for their propagation.

For example : X-ray, Light waves etc.

✦ Equation of a Harmonic Wave:

Harmonic wave are generated by sources that execute simple harmonic motion.

A Harmonic wave travelling along the positive (+ve) direction of x-axis is represented by

y=A sin (ωt–kx)

=A sin {2π(t/T–x/λ)}

=A sin {2π/λ(vt–x)}

Where,

☞ y = displacement of the particle of the medium at a location X at time t

☞ A = amplitude of the wave

☞ λ = wavelength

☞ T = time period

☞ v = velocity of the wave in the

medium, Ʋλ

☞ ⍵ = angular frequency, 2π/T

☞ k = angular wave number, 2π/λ

If the wave is travelling along the negative (–ve) direction of x-axis then

y = A sin (⍵t + Kx)

Differential equation of wave motion:

d²y/dx² = 1/v² × d²/dt²

Relation between wave velocity and particle velocity:

y = A sin (⍵t – kx) .....(i)

Particle velocity,

Vp = dy/dt = A⍵ cos(ωt–kx) ......(ii)

Slope of displacement curve,

dy/dx = –Ak cos (ωt–kx) ......(iii)

When we divide equation (ii) by equation (iii), we get the following

Vₚ = –v. dy/dx

☞ λ = Ʋ2π/ω = ƲT.

☞ k = 2π/λ

= 2πv/Ʋ

= ω/Ʋ.

Relation between phase difference, path difference and time difference :

☞Phase difference of 2π radian is equivalent to a path difference λ and a time difference of period T.

☞Phase difference = (2π/λ)× path difference

Φ = (2π/λ)×x

x= (λ/2π)×Φ

☞Phase difference =(2π/T)× time difference

Φ = (2π/T) ×t

t = (T/2π)×Φ

☞Time difference = (T/λ)×path difference

t = (T/λ)×x

x= (λ/T)×T

✦ Speed of Sound in a gas

Newton's formula

Laplace's correction

Did you know 🤔🤔

For a wave

v = fλ

The velocity of sound in air

Particle velocity is given by vp = dx/dt. It changes with time. The wave velocity is the velocity with which disturbance travel in the medium and is given by vw = ω/k.

When a wave reflects from denser medium, the phase change is π and when the wave reflects from rarer medium, the phase change is zero.

In a tuning fork, the wave produced in the prongs is transverse whereas in the stem is longitudinal.

A medium in which the speed of wave is independent of the frequency of the waves is called non-dispersive.

For example Air is non-dispersive. medium for the sound waves.

Transverse waves can propagate in the medium with shear modulus of elasticity.

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