Course Content
Class 11 Physics Chapter 4 Motion In A Plane
4 Motion in a plane 4.1 Introduction 4.2 Scalars and vectors 4.3 Multiplication of vectors by real numbers 4.4 Addition and subtraction of vectors – graphical method 4.5 Resolution of vectors 4.6 Vector addition – analytical method 4.7 Motion in a plane 4.8 Motion in a plane with constant acceleration 4.9 Relative velocity in two dimensions 4.10 Projectile motion 4.11 Uniform circular motion
Class 11 Physics Chapter 5 Laws of motion
Section Name Topic Name 5 Laws of motion 5.1 Introduction 5.2 Aristotle’s fallacy 5.3 The law of inertia 5.4 Newton’s first law of motion 5.5 Newton’s second law of motion 5.6 Newton’s third law of motion 5.7 Conservation of momentum 5.8 Equilibrium of a particle 5.9 Common forces in mechanics 5.10 Circular motion 5.11 Solving problems in mechanics
Class 11 Physics Chapter 6 Work Energy and Power
Section Name Topic Name 6 Work Energy and power 6.1 Introduction 6.2 Notions of work and kinetic energy : The work-energy theorem 6.3 Work 6.4 Kinetic energy 6.5 Work done by a variable force 6.6 The work-energy theorem for a variable force 6.7 The concept of potential energy 6.8 The conservation of mechanical energy 6.9 The potential energy of a spring 6.10 Various forms of energy : the law of conservation of energy 6.11 Power 6.12 Collisions
Class 11 Physics Chapter 7 Rotation motion
Topics Introduction Centre of mass Motion of COM Linear Momentum of System of Particles Vector Product Angular velocity Torque & Angular Momentum Conservation of Angular Momentum Equilibrium of Rigid Body Centre of Gravity Moment of Inertia Theorem of perpendicular axis Theorem of parallel axis Moment of Inertia of Objects Kinematics of Rotational Motion about a Fixed Axis Dynamics of Rotational Motion about a Fixed Axis Angular Momentum In Case of Rotation about a Fixed Axis Rolling motion
Class 11 Physics Chapter 9 mechanics properties of solid
Section Name Topic Name 9 Mechanical Properties Of Solids 9.1 Introduction 9.2 Elastic behaviour of solids 9.3 Stress and strain 9.4 Hooke’s law 9.5 Stress-strain curve 9.6 Elastic moduli 9.7 Applications of elastic behaviour of materials
Class 11 Physics Chapter 11 Thermal Properties of matter
Section Name Topic Name 11 Thermal Properties of matter 11.1 Introduction 11.2 Temperature and heat 11.3 Measurement of temperature 11.4 Ideal-gas equation and absolute temperature 11.5 Thermal expansion 11.6 Specific heat capacity 11.7 Calorimetry 11.8 Change of state 11.9 Heat transfer 11.10 Newton’s law of cooling
Class 11 Physics Chapter 14 Oscillations
Section Name Topic Name 14 Oscillations 14.1 Introduction 14.2 Periodic and oscilatory motions 14.3 Simple harmonic motion 14.4 Simple harmonic motion and uniform circular motion 14.5 Velocity and acceleration in simple harmonic motion 14.6 Force law for simple harmonic motion 14.7 Energy in simple harmonic motion 14.8 Some systems executing Simple Harmonic Motion 14.9 Damped simple harmonic motion 14.10 Forced oscillations and resonance
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About Lesson


Beats is the phenomenon caused by two sound waves of nearly same frequencies and amplitudes travelling in the same direction.

For example:-

  • Tuning of musical instruments like piano, harmonium etc. Before we start playing on these musical instruments they are set against the standard frequency. If it is not set a striking noise will keep on coming till it is set.


  • Consider only the time dependent and not the position dependent part of the wave.
  • s1=a cos ω1t and s2=a cos ω2t; where amplitude and phase of the waves are same,but the frequencies are varying. Also considering ω1> ω2.
  • When these 2 waves superimpose s= s1+ s2=a[cos ω1t + cos ω2t]
  • By simplifying , 2a (cos(ω1 – ω2)/2)t cos(ω1 + ω2)/2)t)
  • =>ω1 – ω2 is very small as ω1> ω2.Let (ω1 – ω)=ωb
  • =>ω1 + ωis very large. Let (ω1 + ω)=ωa
  • s= 2a cos ωbt cos ωat
  • cosωat will vary rapidly with time and 2acosωbt will change slowly with time.
  • Therefore we can say 2acosωbt = constant. As a result 2acosωbt = amplitude as it has small angular variation.

Problem:- Two sitar strings A and Bplaying the note ‘Dha’ are slightly out oftune and produce beats of frequency 5 Hz.The tension of the string B is slightlyincreased and the beat frequency is foundto decrease to 3 Hz. What is the originalfrequency of B if the frequency of A is 427 Hz?

Answer:-  Increase in the tension of a stringincreases its frequency. If the original frequencyof B (νB) were greater than that of A (νA), furtherincrease in νB should have resulted in anincrease in the beat frequency. But the beatfrequency is found to decrease. This shows thatνB< νA. Since νA – νB = 5 Hz, and νA = 427 Hz, weget νB = 422 Hz.

Doppler’s Effect

  • Doppler Effect is the phenomenon of motion-related frequency change.
  • Consider if a truck is coming from very far off location as it approaches near our house, the sound increases and when it passes our house the sound will be maximum. And when it goes away from our house sound decreases.
  • This effect is known as Doppler Effect.
  • A person who is observing is known as Observer and object from where the sound wave is getting generated it is known as Source.
  • When the observer and source come nearer to each other as a result waves get compressed. Therefore wavelength decreases and frequency increases.
  • Case 1:- stationary observer and moving source
  • Let the source is located at a distance L from the observer.
  • At any time t1, the source is at position P1.
  • Time taken by the wave to reach observer =L/v where v=speed of the sound wave.
  • After some time source moves to position P0 in time T0.
  • Distance between P1 and P0 =vsTo where vs is the velocity of the source.
  • Let t2be the time taken by the second wave to reach the observer
    • Total time taken by the for the second wave to be sent to the observer = To +( L+vsTo)/v
    • Total time taken by the for the third wave to be sent to the observer=2To +( L+2vsTo)/v
    • Therefore for nth point tn+1 =nTo +( L+nvsTo)/v
    • =>In time tn+1the observer captures n waves.
  • Total time taken by the waves to travel Time period T= (tn+1 – t1)/n
  • =To +(vsTo)/v =>T=To(1+vs/v)
  • Or v= 1/T
  • =>v = v0(1+vs/v)-1
  • By using binomial Theorem,v= v(1- vs/v)
  • If the source is moving towards the observer the expression will become v= v(1+ vs/v)
  • Case 2:- moving observer and stationary source
  • As the source is not moving therefore vs is replaced by -v0.
  • Therefore v= v(1+ v0/v)
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