Undergraduate
  1. Classical mechanics  1.1. dynamics  1.1.1. Motion in one dimension  1.1.2. Motion in two dimensions  1.1.3. projectile motion  1.1.4. Relative speed  1.1.5. Uniform circular motion  1.1.6. Non-uniform circular motion  1.1.7. Reference frames and transformations  1.2. Newton's Laws of Motion  1.2.1. First law of motion  1.2.2. Second law of motion  1.2.3. Third Law of Motion  1.2.4. Applications of Newton's Laws  1.2.5. Friction and its types  1.2.6. Free Body Diagram  1.2.7. Constraints and pseudo-forces  1.3. Work and Energy  1.3.1. work done by the force  1.3.2. Work–energy theorem  1.3.3. Kinetic energy  1.3.4. Potential energy in classical mechanics  1.3.5. Conservative and non-conservative forces  1.3.6. Energy Conservation  1.3.7. Power and efficiency  1.4. Speed and collisions  1.4.1. Linear momentum  1.4.2. Conservation of momentum  1.4.3. Impulse and impact force  1.4.4. Elastic and inelastic collision  1.4.5. Center of mass and speed  1.4.6. Rocket Propulsion  1.5. Rotational motion  1.5.1. Torque and Angular Momentum  1.5.2. Moment of inertia  1.5.3. Rotational Kinematics  1.5.4. Rotational Energy  1.5.5. Rolling Motion  1.5.6. Precession and gyroscopic motion  1.6. Gravitational force  1.6.1. Newton's law of universal gravitation  1.6.2. Gravitational potential energy  1.6.3. Orbital mechanics  1.6.4. Kepler's laws of planetary motion  1.6.5. Gravitational field and potential  1.7. Fluid mechanics  1.7.1. Pressure and Pascal's Principle  1.7.2. Buoyancy and Archimedes' principle  1.7.3. Fluid Dynamics and Bernoulli's Principle  1.7.4. Viscosity and Poiseuille's law  1.7.5. Surface tension and capillarity  1.8. Oscillations and waves  1.8.1. Simple Harmonic Motion  1.8.2. Damped and driven oscillations  1.8.3. Coupled oscillations and common modes  1.8.4. Wave properties and types  1.8.5. Sound Waves and the Doppler Effect  1.8.6. Wave interference and superposition
  2. Electromagnetism  2.1. Electrostatics  2.1.1. Electric charge and properties  2.1.2. Coulomb's law  2.1.3. Electric field and electric potential  2.1.4. Gauss's Law  2.1.5. Capacitance and Dielectric  2.1.6. Electric dipole and potential energy  2.2. Electric circuits  2.2.1. Current and Resistance  2.2.2. Ohm's law  2.2.3. Kirchhoff's Laws  2.2.4. RC Circuit  2.2.5. AC Circuits and Reactance  2.2.6. Electric power and energy  2.3. Magnetism  2.3.1. Magnetic Fields and Forces  2.3.2. Ampere's Law  2.3.3. Magnetic dipole moment  2.3.4. Biot-Savart law  2.3.5. Magnetic Materials and Hysteresis  2.4. Electromagnetic induction  2.4.1. Faraday's Law  2.4.2. Lenz's law  2.4.3. Self and mutual induction  2.4.4. Transformers and Inductive Circuits  2.5. Maxwell's equations  2.5.1. Gauss's law for electricity  2.5.2. Gauss's law for magnetism  2.5.3. Faraday's law of induction  2.5.4. Ampere-Maxwell law  2.5.5. Electromagnetic waves
  3. Thermodynamics  3.1. Laws of Thermodynamics  3.1.1. Zeroth law of thermodynamics  3.1.2. First law of thermodynamics  3.1.3. Second Law  3.1.4. Third Law  3.2. Heat and work  3.2.1. Heat transfer (conduction, convection, radiation)  3.2.2. Thermal expansion  3.2.3. Heat engines and refrigerators  3.2.4. Carnot cycle and efficiency  3.3. Statistical mechanics  3.3.1. Maxwell–Boltzmann distribution  3.3.2. Entropy and Probability  3.3.3. Partition function  3.3.4. Fermi–Dirac and Bose–Einstein statistics
  4. Optics  4.1. Geometrical Optics  4.1.1. Reflection and Refraction  4.1.2. Mirrors and lenses  4.1.3. Optical Instruments  4.1.4. Fermat's principle  4.2. Wave optics  4.2.1. Interference in wave optics  4.2.2. Diffraction  4.2.3. Polarization  4.2.4. Coherence and holography
  5. Quantum mechanics  5.1. Wave–particle duality  5.1.1. Blackbody radiation in wave–particle duality in quantum mechanics  5.1.2. Photoelectric effect  5.1.3. Compton scattering  5.1.4. De Broglie wavelength  5.2. Schrödinger Equation  5.2.1. Time-independent Schrödinger equation  5.2.2. Particle in a box  5.2.3. Quantum Tunneling  5.2.4. Potential wells and obstacles  5.3. Quantum States  5.3.1. Wave function  5.3.2. Quantum operators  5.3.3. Heisenberg uncertainty principle  5.3.4. Angular momentum and spin
  6. Relativity  6.1. Special relativity  6.1.1. Lorentz transformations  6.1.2. Time expansion and length contraction  6.1.3. Relativistic energy and momentum  6.2. General relativity  6.2.1. Principle of Equivalence  6.2.2. Schwarzschild metric  6.2.3. Gravitational waves  6.2.4. Black holes and event horizons
  7. Solid state physics  7.1. Crystal structure  7.1.1. Bravais lattices  7.1.2. X-ray diffraction  7.1.3. Band theory  7.1.4. Phonons and lattice vibrations  7.2. Electrical and Magnetic Properties  7.2.1. Conductors, Semiconductors and Insulators  7.2.2. Superconductivity  7.2.3. Hall effect
  8. Nuclear and particle physics  8.1. Atomic Structure  8.1.1. Atomic Model  8.1.2. Nuclear binding energy  8.2. Radioactivity  8.2.1. Alpha, beta, gamma decay  8.2.2. Half life  8.2.3. Nuclear Fission and Fusion  8.3. Particle physics  8.3.1. Standard Model  8.3.2. Quarks and Leptons  8.3.3. antimatter  8.3.4. Fundamental interactions
  9. Astrophysics and cosmology  9.1. Stellar evolution  9.1.1. Star formation  9.1.2. Black holes and neutron stars  9.1.3. White dwarfs and supernovae  9.2. Cosmology  9.2.1. The Big Bang Theory  9.2.2. Dark matter and dark energy  9.2.3. Cosmic microwave background

Undergraduate → Classical mechanics → Oscillations and waves ↓


Wave properties and types


Waves are a fascinating aspect of physics, encompassing some of the most fundamental concepts of how energy and information travel through mediums. In classical mechanics, the study of waves is essential, providing insight into both natural phenomena and practical applications in a variety of fields. Let's dive into wave properties and types, explaining these concepts in a way that's easy to understand, even if you're just starting out with the physics of oscillations and waves.

What is a wave?

A wave is a disturbance that travels through space and time, often transferring energy from one place to another. Waves can travel through various mediums, such as air, water and solids, or even through a vacuum, as is the case with electromagnetic waves such as light. Unlike particles, waves can overlap, combine and change without carrying any matter with them.

Basic properties of waves

Before learning about the different types of waves, it is necessary to understand some basic properties that most waves have in common. These include:

  • Wavelength (λ): The distance between two consecutive points on a wave that are in the same phase, such as peak to peak or trough to trough.
  • Frequency (f): The number of wave cycles passing a point per unit of time, usually measured in hertz (Hz).
  • Amplitude (A): The maximum displacement of points on a wave, which corresponds to the energy of the wave.
  • Period (T): The time it takes for one complete wave cycle to pass a given point, the inverse of the frequency (T = 1/f).
  • Wave speed (v): The speed at which the wave propagates through the medium, calculated as v = λf.

The mathematical relationship between these properties can be represented by the formula:
Dimensions Wavelength (λ)

This diagram shows a simple wave, and highlights two important properties of waves: amplitude and wavelength.

Types of waves

Waves can be classified based on various criteria, such as what medium they require to propagate, the direction of particle displacement relative to the wave propagation, and whether they require any physical matter to propagate. Here are the two primary classifications:

Mechanical waves

Mechanical waves require a medium (matter or material) for their propagation. These waves can travel through solids, liquids and gases. Mechanical waves are further divided into two types:

  • Transverse waves: In these waves, the particle displacement is perpendicular to the wave propagation. Water waves and electromagnetic waves like light are examples. Here is a simplified diagram showing a transverse wave:
  • Longitudinal Waves: In these waves, the particle displacement is parallel to the wave propagation. Sound waves in air are a prime example of longitudinal waves. Here is a diagram showing a longitudinal wave:

In the figure above, notice how the density of the lines changes, showing areas of compression and rarefaction in the wave.

Electromagnetic waves

Unlike mechanical waves, electromagnetic waves do not require a medium to propagate; they can travel in a vacuum. These include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Electromagnetic waves are inherently transverse waves.

This diagram presents electromagnetic waves, showing both electric (blue) and magnetic (red) field components oscillating perpendicular to the direction of wave travel.

Behavior of Waves

Waves exhibit different behaviours when they interact with boundaries and other waves. Here are some of the main phenomena:

Reflection

Reflection occurs when a wave hits a boundary and returns. A classic example of this is the echo of a sound wave reflecting off a distant mountain.

Reflection of waves at a fixed end

When a wave reflects from a fixed end, it is reversed. This can be demonstrated using a rope with one end fixed. As the wave pulse travels and hits the fixed end, it is reflected back with an inverted phase:

Reflection of waves at the free end

When dealing with a free end, the wave does not invert after reflection. Imagine a wave in a rope with one end not attached, allowing the pulse to return without inversion:

Refraction

Refraction is the change in the direction of a wave as it travels from one medium to another due to a change in speed. A common example is the bending of light as it enters water from air.

Diffraction

Diffraction occurs when a wave bends around obstacles or spreads out after passing through narrow holes. Think about how you can hear someone talking even if you are behind a wall.

Interference

When two or more waves overlap, they combine to form a new wave pattern. This can be constructive (amplitudes add together) or destructive (amplitudes subtract from each other). Observation of water waves where two stones are thrown shows interference.

Standing waves

When two waves with the same frequency and amplitude travel in opposite directions, they can combine to form stationary waves. These waves appear stationary, with nodes (points of no motion) and antinodes (points of maximum motion).

This relationship is important for musical instruments, where vibrating strings or air columns create standing waves, producing harmonics and resonance. Try to imagine standing waves on a string, where the fixed ends act as nodes and waves oscillate between them:

Summary

Understanding the properties and types of waves is important in physics and broader scientific disciplines. We have explored many fundamental aspects related to the basic properties, types, behaviors of waves, and more. This knowledge forms an important foundation for further exploration in specific fields such as optics, acoustics, and electromagnetic theory.


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Wave properties and types

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