Grade 12
  1. Advanced mechanics  1.1. Dynamics  1.1.1. Motion in two and three dimensions  1.1.2. Advanced Projectile Motion and Range Equations  1.1.3. Relative motion in different reference frames  1.1.4. Motion of charged particles in electric and magnetic fields  1.1.5. Non-uniformly accelerated motion in multiple dimensions  1.2. Dynamics  1.2.1. Newton's laws and applications in non-inertial frames  1.2.2. Dynamics of particle systems  1.2.3. Non-conservative forces and energy dissipation  1.2.4. Momentum in variable mass systems (rocket momentum)  1.2.5. Lagrangian and Hamiltonian Mechanics (Introduction)  1.3. Work, Energy and Power  1.3.1. Work done by non-conservative forces  1.3.2. Power in rotational and translational motion  1.3.3. Advanced Conservation Laws and Applications  1.3.4. Potential energy surface and stability  1.4. Advanced rotational speed  1.4.1. Torque in three dimensions  1.4.2. Moment of inertia for irregular bodies  1.4.3. Gyroscopic motion and precession  1.4.4. Rotational work–energy theorem  1.4.5. Euler's equations of rotational motion  1.5. Gravitational force  1.5.1. Advanced Orbital Mechanics  1.5.2. Lagrange points and stability of orbits  1.5.3. Gravitational time dilation  1.5.4. Escape velocity and energy considerations  1.5.5. Tidal force and the Roche limit
  2. Fluid mechanics and thermodynamics  2.1. Fluid dynamics  2.1.1. Applications of Bernoulli's Principle  2.1.2. Navier-Stokes equations and fluid resistance  2.1.3. Turbulent vs. Laminar Flow  2.1.4. Surface tension and capillary action  2.2. Advanced Thermal Physics  2.2.1. Thermodynamic equilibrium and heat engines  2.2.2. Entropy and the Second Law of Thermodynamics  2.2.3. Maxwell's demon and statistical thermodynamics  2.2.4. Thermodynamic potential and free energy
  3. Oscillations and waves  3.1. Advanced Simple Harmonic Motion  3.1.1. Coupled oscillations and common modes  3.1.2. Damped and driven oscillations  3.1.3. Phase space and resonance  3.1.4. Anharmonic oscillations  3.2. Wave motion  3.2.1. Advanced wave equations and dispersion  3.2.2. Shock Waves and Sonic Booms  3.2.3. Doppler effect in electromagnetic waves  3.2.4. Wave–particle duality
  4. Electromagnetism  4.1. Electrostatics  4.1.1. Gauss's law in unilateral charge distribution  4.1.2. Electric potential for complex charge configuration  4.1.3. Electrostatic energy and self-energy of a system  4.1.4. Dielectrics and Polarization  4.2. Current Electricity  4.2.1. Advanced Circuit Analysis (Thevenin and Norton theorems)  4.2.2. RC, RL and RLC circuits in AC and DC  4.2.3. Superconductivity and applications  4.3. Advanced Magnetism and Electromagnetic Induction  4.3.1. Magnetic fields in conductors and plasma  4.3.2. Lenz's law in time-dependent magnetic fields  4.3.3. Eddy Currents and Applications  4.3.4. Magnetic dipole moment and torque on electric current loops  4.4. Alternating Current and Electromagnetic Waves  4.4.1. LC Circuits and Resonance  4.4.2. Maxwell's equations and electromagnetic wave transmission  4.4.3. Applications of Electromagnetic Waves  4.4.4. Polarization and reflection of EM waves
  5. Optics  5.1. Geometrical Optics  5.1.1. Aberrations in optical systems  5.1.2. Advanced lens and mirror formulas  5.1.3. Optical Instruments and Adaptive Optics  5.2. Wave optics  5.2.1. Diffraction at single and multiple slits  5.2.2. Optical Coherence and Interferometry  5.2.3. Holography and applications
  6. Modern and quantum physics  6.1. Special relativity  6.1.1. Time expansion and length contraction  6.1.2. Relativistic energy and mass  6.1.3. Relativistic Doppler effect  6.2. Quantum mechanics  6.2.1. Schrödinger equation and wave function  6.2.2. Quantum tunneling and applications  6.2.3. Heisenberg uncertainty principle  6.2.4. Quantum superposition and entanglement  6.3. Nuclear physics  6.3.1. Binding energy and mass defect  6.3.2. Neutrino physics and beta decay  6.3.3. Nuclear Fission and Fusion  6.4. Particle physics  6.4.1. Standard Model and fundamental interactions  6.4.2. The Higgs boson and symmetry breaking  6.4.3. Antimatter and CP violation
  7. Astrophysics and cosmology  7.1. General relativity and gravity  7.1.1. Einstein's field equations  7.1.2. Gravitational waves and their detection  7.1.3. Black holes and event horizons  7.2. Cosmology  7.2.1. Dark matter and dark energy  7.2.2. Cosmic microwave background radiation  7.2.3. The expansion of the universe and Hubble's law

Grade 12 ↓


Oscillations and waves


In Class 12 Physics, understanding oscillations and waves is important to explain a wide range of physical phenomena occurring in nature and technology. This lesson will explore these concepts in detail using simple language and various examples.

What are oscillations?

Oscillations are repetitive changes in some measure, usually time. When an object repeats the same motion at regular time intervals, it is said to be oscillating. The perfect example of an oscillating system is a simple pendulum in a clock.

Imagine a pendulum swinging back and forth. Each complete cycle of its motion—from the highest point on one side to the highest point on the other side and back—is one oscillation.

"Pendulum oscillations"
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Here are some key terms related to oscillations:

  • Amplitude: The maximum extent of the vibration or oscillation, measured from the equilibrium position. In our pendulum example, this would be the height from the lowest point to the highest point.
  • Period: The time it takes for one complete cycle of oscillation. In the case of a pendulum, this is the time it takes to swing from side to side and back again.
  • Frequency: The number of oscillations per unit time. If the pendulum swings back and forth once every second, its frequency would be 1 Hertz (Hz).
  • Phase: A measure of the oscillator's position in the cycle.

Understanding waves

Waves are disturbances that transfer energy from one place to another without moving matter. They can be found everywhere, whether it is the light that we see or the sound that we hear. Let us learn about the structure of a wave in detail.

Dimensions Wavelength

Waves can be classified into two main types: transverse waves and longitudinal waves.

  • Transverse waves: The oscillations are perpendicular to the direction of the wave. A classic example is a wave on a string.
  • Longitudinal waves: The oscillations occur in the direction of the wave. Sound waves are longitudinal waves.

Mathematics of waves and oscillations

We can describe oscillations and waves using mathematical equations. These help us predict behavior and properties. For example, simple harmonic motion (SHM) is represented by the function:

x(t) = A cos(ωt + φ)

Where:

  • x(t) is the displacement at time t.
  • A is the dimension.
  • ω (omega) is the angular frequency, related to the frequency by ω = 2πf.
  • φ (phi) is the phase constant.

For a wave, the wave equation is structured like this:

y(x, t) = A sin(kx - ωt + φ)

Where:

  • y is the displacement.
  • k is the wavenumber, defined as 2π/λ (lambda, wavelength).
  • Other symbols are as described previously.

Energy in oscillations and waves

Oscillating systems store energy. Consider the pendulum again. At its highest point, it has maximum potential energy and no kinetic energy. As it swings downward, the potential energy is converted into kinetic energy.

Energy in waves is transferred through space. Water waves clearly demonstrate energy transfer as they move across the surface of a pond.

The energy associated with a wave is related to its amplitude. Specifically, the energy carried by a wave is proportional to the square of its amplitude:

E ∝ A²

Sound waves

Sound waves are a type of longitudinal waves. When you speak, your larynx creates a pressure difference in the air, which travels to the listener's ear and makes the eardrum vibrate.

Sound features include:

  • Pitch: Relating to the frequency of a sound. Higher frequencies correspond to higher pitches.
  • Loudness: Relating to the amplitude of a sound wave.
  • Timbre: Also known as tone quality or color, this arises from waveform complexity.

Light waves

Light waves are electromagnetic waves, which means they don't need a medium to travel. This is why light can travel in the vacuum of space.

The properties of light waves include:

  • The speed of light in a vacuum is about 3 x 108 m / s.
  • Reflection: Light bounces off surfaces.
  • Refraction: Light bends when passing through different mediums.
  • Diffraction: Light spreads out as it passes through narrow holes.
Light wave

Superposition and interference

When two or more waves collide with each other, they superimpose on each other. The principle of superposition states that the resultant wave is the sum of the individual waves.

If the wave crests meet crests and troughs meet troughs, constructive interference occurs, producing a wave of greater amplitude. If those crests meet troughs, destructive interference occurs, causing the amplitude to decrease.

Wave 1 Wave 2 Resultant

Echo

Resonance occurs when a system is driven at a frequency that matches its natural frequency, resulting in large amplitude oscillations. A familiar example of resonance is pushing a swing. If the push is timed correctly, the swing gets louder and louder.

Applications in technology

Understanding vibrations and waves is important in a variety of technological applications. For example, in medical imaging, ultrasound uses sound waves to create images of the body's internal structures.

In communications, radio, television, and mobile signals rely on electromagnetic waves. Engineers design antennas and receivers based on wave principles to ensure signal clarity and transmission efficiency.

Summary

Oscillations and waves are fundamental concepts in physics, providing insight into natural phenomena and enabling modern technological advancements. From simple pendulums to complex wave interactions, they reflect the beautiful nature of energy transfer in the universe.

By studying oscillations and waves, we gain deeper knowledge about the world, leading to innovations that improve daily life and broaden scientific understanding.


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Oscillations and waves

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