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

The principle of superposition of waves

  • Principle of superposition of waves describes how the individual waveforms can be algebraically added to determine the net waveform.
  • Waveform tells about the overall motion of the wave.It does not tell about individual particles of the wave.
  • Suppose we have 2 waves and
  • Example of superposition of waves is Reflection of waves.
  • Mathematically: –


  • Consider 2waves which are in phase with each other. They have the same amplitude, same angular frequency, and same angular wave number.
  • If wave 1 is represented by y1(x, t) =a sin (kx – ωt).
  • Wave 2 is also represented by y2(x, t) =a sin (kx – ωt).
  • By the principle of superposition the resultant wave (2a sin (kx – ωt)) will also be in phase with both the individual waves but the amplitude of the resultant wave will be more.


  • Consider when the two waves are completely out of phase.i.e. φ = π
  • If wave 1 is represented by y1(x, t) =a sin (kx – ωt).
  • Wave 2 is represented by y2(x, t) =a sin (kx – ωt+ π).
  • =>y2=asin(π-(-kx+ ωt) =>y2=-a sin(kx- ωt)
  • Therefore by superposition principle y=y1+y2=0

Reflection at rigid boundary

  • Consider a string which is fixed to the wall at one end. When an incident wave hits a wall,it will exerta force on the wall.
  • By Newton’s third law, the wall exerts an equal and opposite force of equal magnitude on the string.
  • Since the wall is rigid wall won’t move, therefore no wave is generated at the boundary.This implies the amplitude at the boundary is 0.
  • As both the reflected wave and incident wave are completely out of phase at the boundary.Therefore φ=π.
  • Therefore, yi(x, t) = a sin (kx – ωt),
  • yr(x, t) = a sin (kx + ωt + π) = – a sin (kx + ωt)
  • By superposition principle y= y+ yr =0
  • Conclusion: –
    • The reflection at the rigid body will take place with a phase reversal of π or 180.

Standing (Stationary) Waves

  • A stationary wave is a wave which is not moving,i.e. it is at rest.
  • When two waves with the same frequency,wavelengthand amplitude travelling in opposite directions will interfere they produce a standing wave.
  • Explanation:-
    • Consider Ist wave in the figure and suppose we have a rigid wall which does not move. When anincident wave hits the rigid wall it reflects back with a phase difference of π.
    • Consider IInd wave in the figure, when the reflected wave travels towards the left there is another incident wave which is coming towards right.
    • The incident wave is continuously coming come from left to right and the reflected wave will keep continuing from right to left.
    • At some instant of time there will be two waves one going towards right and one going towards left as a result these two waves will overlap and form a standing wave.
  • Mathematically:
  • Wave travelling towards left yl(x,t) =a sin(kx– ωt) and towards right yr(x,t) =a sin (kx + ωt)
  • The principle of superposition gives, for the combined wave
  • y (x, t) = yl(x, t) + yr(x, t)= a sin (kx – ωt) + a sin (kx + ωt)
  • y(x,t)= (2a sin kx) cos ωt (By calculating and simplifying)
  • The above equation represents the standing wave expression.
  • Amplitude = 2a sin kx.
    • The amplitude is dependent on the position of the particle.
    • The cos ωt represents the time dependent variation or the phase of the standing wave.

Difference between the travelling wave and stationary wave

Travelling Wave(Progressive Wave) Stationary Wave (Standing wave)
Waveform moves. Movement of the waveform is always indicated by the movement of the peaks of the wave. Waveform doesn’t move.Peaks don’t move.
Wave amplitude is same for all the elements in the medium. Denoted by ‘A’. Wave amplitude is different for different elements.Denoted by asinkx.
Amplitude is not dependent on the position of the elements of the medium. Amplitude is dependent on the position of the elements of the medium.
y(x,t)=asin(kx– ωt + φ ) y(x,t)=2asin(kx)cos(ωt)
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