Grade 11
  1. Mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two and three dimensions  1.1.3. Displacement and Distance  1.1.4. Speed and Velocity  1.1.5. Acceleration and deceleration  1.1.6. Graphical analysis of motion  1.1.7. Equations of motion (advanced derivations)  1.1.8. Free fall and terminal velocity  1.1.9. Projectile motion  1.1.10. Relative velocity in one and two dimensions  1.1.11. Motion of a car on an inclined plane  1.2. Dynamics  1.2.1. Newton's laws of motion and their applications  1.2.2. Inertia and Newton's first law  1.2.3. Force and types of force  1.2.4. Static and kinetic friction  1.2.5. Circular motion and centripetal acceleration  1.2.6. Non-uniform circular motion  1.2.7. Banking of roads and curves  1.2.8. Momentum and Impulse  1.2.9. Conservation of momentum in one and two dimensions  1.2.10. Applications of Newton's Third Law  1.3. Work, Energy and Power  1.3.1. Work done by a constant and variable force  1.3.2. Work–energy theorem  1.3.3. Kinetic and potential energy  1.3.4. Gravitational and elastic potential energy  1.3.5. Conservation of mechanical energy  1.3.6. Power and instantaneous power  1.3.7. Efficiency of machines  1.3.8. Work done by conservative and non-conservative forces  1.4. Rotational motion  1.4.1. Torque and angular acceleration  1.4.2. Rotational equilibrium  1.4.3. Moment of inertia and its applications  1.4.4. Angular momentum and its conservation  1.4.5. Kinetic energy of rolling motion and rotation  1.4.6. Parallel and Perpendicular Axis Theorem  1.4.7. Dynamics of rotational motion
  2. Gravitational force  2.1. Universal gravitation  2.1.1. Newton's law of universal gravitation  2.1.2. Gravitational field and potential  2.1.3. Change in acceleration due to gravity  2.1.4. Kepler's laws of planetary motion  2.1.5. Orbital mechanics and satellites  2.1.6. Escape velocity and orbital velocity  2.1.7. Weightlessness and free fall  2.1.8. Gravitational potential energy and energy in orbits  2.1.9. Black holes and gravitational lensing
  3. Properties of matter  3.1. Fluid mechanics  3.1.1. Density and pressure in liquids  3.1.2. Pascal's theory and applications  3.1.3. Archimedes' Principle and Buoyancy  3.1.4. Bernoulli's equation and applications  3.1.5. Continuity equation and the Venturi effect  3.1.6. Surface tension and capillarity  3.1.7. Viscosity and Poiseuille's Law  3.1.8. Reynolds number and turbulence  3.2. Elasticity and deformation  3.2.1. Hooke's law and the stress-strain relation  3.2.2. Elastic modulus and applications  3.2.3. Deformation and yield strength of solids
  4. Thermal physics  4.1. Heat and temperature  4.1.1. Thermometric properties and temperature scale  4.1.2. Thermal expansion of solids, liquids and gases  4.1.3. Heat transfer system  4.1.4. Specific heat capacity and calorimetry  4.1.5. Latent heat and phase change  4.2. Kinetic theory of gases  4.2.1. Molecular model of gases  4.2.2. Kinetic explanation of temperature  4.2.3. Ideal Gas Equation and Deviations  4.2.4. Mean free path and Maxwell–Boltzmann distribution  4.3. Laws of Thermodynamics  4.3.1. Zeroth Law and Thermal Equilibrium  4.3.2. First Law and Internal Energy  4.3.3. The Second Law and Entropy  4.3.4. Carnot cycle and heat engines  4.3.5. Refrigerators and heat pumps
  5. Waves and oscillations  5.1. Simple Harmonic Motion  5.1.1. Equations of SHM  5.1.2. Energy in SHM  5.1.3. Damped and forced oscillations  5.1.4. Resonance and applications  5.1.5. Pendulum and spring-mass system  5.2. Wave motion  5.2.1. Types of mechanical waves  5.2.2. Wave motion and energy transport  5.2.3. Superposition Principle and Standing Waves  5.2.4. Reflection, Refraction and Diffraction  5.2.5. Doppler effect in sound and light  5.2.6. Pulsations and interference
  6. Electricity and Magnetism  6.1. Electrostatics  6.1.1. Electric charge and conservation  6.1.2. Coulomb's law and its applications  6.1.3. Electric field and electric flux  6.1.4. Electric potential and potential energy  6.1.5. Capacitance and Energy Stored in a Capacitor  6.2. Current Electricity  6.2.1. Ohm's law and electrical resistance  6.2.2. Resistivity and temperature dependence  6.2.3. Kirchhoff's Laws and Circuit Analysis  6.2.4. Electrical power and efficiency  6.2.5. Combination of resistors  6.3. Magnetism and Electromagnetism  6.3.1. Magnetic fields and their sources  6.3.2. Magnetic force on moving charges  6.3.3. Electromagnetic induction  6.3.4. Faraday's and Lenz's laws  6.3.5. Inductance and Transformer  6.3.6. Alternating current and its applications
  7. Optics  7.1. Reflection and Refraction  7.1.1. laws of reflection and refraction  7.1.2. Mirrors and lenses  7.1.3. Total internal reflection and optical fiber  7.2. Wave optics  7.2.1. Interference and Diffraction  7.2.2. Young's double-slit experiment  7.2.3. Polarization of light
  8. Modern Physics  8.1.1. Photoelectric effect and Einstein's theory  8.1.2. Wave–particle duality  8.1.3. Heisenberg's uncertainty principle  8.1.4. Compton Effect  8.2. Atomic and Nuclear Physics  8.2.1. Atomic model and energy levels  8.2.2. Radioactive decay and half-life  8.2.3. Nuclear Fission and Fusion
  9. Electronics and Communication  9.1. Semiconductors  9.1.1. pn junction and diode  9.1.2. Transistors and Logic Gates  9.1.3. Integrated Circuits and Applications  9.2. Communication Systems  9.2.1. Basics of Analog and Digital Communication  9.2.2. Wireless and Optical Communication  9.2.3. Modulation and Demodulation

Grade 11 ↓


Waves and oscillations


The study of waves and oscillations is an integral part of physics. These concepts are fundamental in describing a variety of phenomena in science and engineering. From light ripples on a pond to the sound of musical instruments and even the electromagnetic waves that enable wireless communication, waves and oscillations are all around us. Understanding them can provide insights into how the universe behaves at both the macroscopic and microscopic levels.

Introduction to waves

A wave is a disturbance that travels from one place to another through a medium or vacuum. The medium can be a solid, liquid, gas, or even the vacuum of space. Waves transfer energy from one point to another without the physical transfer of particles from one place to another.

Types of waves

Waves can be classified based on the direction of particle displacement with respect to wave propagation:

1. Mechanical waves

These require a medium to travel. Examples include sound waves, seismic waves, and water waves.

Longitudinal waves

In longitudinal waves the particles of the medium vibrate parallel to the direction of wave propagation. Sound waves in air are a classic example of this.

        Example: Sound waves in air, compressions and rarefactions.
Pressure Sparring
Transverse waves

In transverse waves the particles of the medium move perpendicular to the direction of wave propagation. Light waves and waves on a string are typical examples of this.

        Example: Waves on a string, water surface waves.

2. Electromagnetic waves

Electromagnetic waves do not require a medium to propagate. They can also travel through a vacuum. Examples include light, radio waves, and X-rays.

Wave characteristics

Understanding waves requires knowledge of several key characteristics:

Wavelength ( λ )

Wavelength is the distance between successive crests or troughs in a wave. It determines the length of the wave and is measured in meters.

Frequency ( f )

Frequency refers to how many times the particles of a medium vibrate when a wave passes through it. It is measured in Hertz (Hz), which is equal to cycles per second.

Dimensions

The amplitude of a wave is the maximum displacement of the particles of the medium from their equilibrium position. It represents the energy and intensity of the wave.

Wave speed

The speed of a wave is the distance travelled per unit time by a point (such as a crest) on the wave. The speed ( v ) of a wave can be calculated using the formula:

        v = f * λ

where v is the speed of the wave, f is the frequency, and λ is the wavelength.

Introduction to oscillation

Oscillations are back-and-forth movements at a regular interval. A classic example of an oscillating system is a simple pendulum. When it is displaced from its equilibrium position, it experiences a force that tends to move it back towards equilibrium, creating an oscillatory motion.

Simple harmonic motion (SHM)

Simple harmonic motion is a type of oscillation in which the restoring force is proportional to the displacement and acts opposite to the direction of displacement. SHM is characterized by oscillations having a sinusoidal waveform.

Features of SHM

  • Equilibrium position: The position where the net force on the system is zero.
  • Amplitude ( A ): Maximum displacement from the equilibrium position.
  • Period ( T ): The time taken in one complete cycle of oscillation.
  • Frequency ( f ): The number of oscillations per unit time. It is the inverse of the period.
        f = 1 / T

Mathematical representation of SHM

Motion can be described using a sine or cosine function. If x(t) represents displacement as a function of time, then:

        x(t) = A * cos(ωt + φ)

where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.

The angular frequency is related to the frequency and period as follows:

        ω = 2πf = 2π/T

Energy in SHM

In SHM the energy is continuously transformed between potential energy and kinetic energy while the total mechanical energy remains constant.

Practical examples and applications

Pendulum

The pendulum is one of the most common examples of oscillations. The time period of the pendulum depends on its length and the acceleration due to gravity as shown below:

        T = 2π √(L/g)

Where L is the length and g is the acceleration due to gravity.

Mass-spring system

Another classic example of SHM is a mass attached to a spring. According to Hooke's law, the force exerted by the spring is proportional to the displacement:

        F = -kx

Where k is the spring constant, and x is the displacement.

The time period of oscillation for a mass m on a spring is given by:

        T = 2π √(m/k)

Waves in everyday life

From the music we listen to, the light we see every day, and the radio waves that carry data to our phones, understanding waves helps us understand how our technology and environment work.

Conclusion

Waves and vibrations are everywhere around us and form the backbone of many scientific theories and techniques. From understanding the nature of sound and light to the behaviour of quantum particles, the principles of waves and vibrations form the basis of many advances in science and technology.


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Waves and oscillations

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