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

Nodes and Antinodes of Standing Wave

  • The amplitude of a standing wave doesn’t remain the same throughout the wave.
  • It keeps on changing as it is a function of x.
  • At certain positions the value of amplitude is maximum and at certain positions the value of amplitude is 0.
  • Nodes: – Nodes represent the positions of zero amplitude.
  • Antinodes: – Antinodes represent the positions of maximum amplitude.


  • At nodes, amplitude is 0.
  • In case of the standing wave amplitude is given as :- 2asinkx
  • => 2asinkx = 0 ,=>sinkx = 0,=>sinkx =sin n π => kx=n π
  • The value of x represents position of nodes where amplitude is 0.
  • x=(nπ)/k … equation(i)
  • From the definition of k=(2π)/λ … equation(ii)
  • The position of nodes is represented by: –x=(n λ)/2from(i) and (ii),where n=1, 2, 3…
  • Note: –Half a wavelength (λ/2) separates two consecutive nodes.

Nodes and Antinodes: system closed at both ends

  • System closed at both ends means both the ends are rigid boundaries.
  • Whenever there is rigid body there is no displacement at the boundary. This implies at boundary amplitude is always 0. Nodes are formed at boundary.
  • Standing waves on a string of length L fixed at both ends have restricted wavelength.
  • This means wave will vibrate for certain specific values of wavelength.
  • At both ends,nodes will be formed.=>Amplitude=0.
  • Expression for node x =(nλ)/2.This value is true when x is 0 and L.
  • When x=L:- L=(nλ)/2 =>λ=(2L)/n ; n=1,2,3,4,…..
  • λ cannot take any value but it can take values which satisfy λ=(2L)/n this expression.
  • That is why we can say that the standing wave on a string which is tied on both ends has the restricted wavelength.
  • As wavelength is restricted therefore wavenumber is also restricted.
  • ν =v/λ (relation between wavelength and frequency)
  • Corresponding frequencies which a standing wave can have is given as: –ν= (vn)/2Lwhere v= speed of the travelling wave.
  • These frequencies are known as natural frequency or modes of oscillations.
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