Waves
1. Introduction to Waves
- Wave: A disturbance that travels through a medium transferring energy without transferring matter.
- Caused by vibrating or oscillating source.
2. Types of Waves
- Mechanical Waves: Require a medium to travel (e.g. sound waves, water waves).
- Electromagnetic Waves: Do not require a medium (e.g. light, radio waves).
3. Transverse and Longitudinal Waves
- Transverse Waves: Particles vibrate perpendicular to direction of wave propagation (e.g. light waves, waves on string).
- Longitudinal Waves: Particles vibrate parallel to wave direction (e.g. sound waves).
4. Wave Parameters
- Wavelength (λ): Distance between two consecutive points in phase.
- Frequency (f): Number of oscillations per second.
- Amplitude (A): Maximum displacement from equilibrium.
- Wave Speed (v): Speed at which wave propagates, v = fλ.
5. Mathematical Representation of Waves
- Displacement of wave at position x and time t: y(x, t) = A sin(kx - ωt + φ)
- Where k = wave number = 2π/λ, ω = angular frequency = 2πf, φ = phase constant
6. Principle of Superposition
- When two or more waves overlap, resultant displacement is sum of individual displacements.
- Leads to interference and formation of standing waves.
7. Reflection and Transmission of Waves
- When wave encounters a boundary, part of wave is reflected, part is transmitted.
- Reflection can be fixed-end (inverts wave) or free-end (no inversion).
8. Standing Waves and Resonance
- Formed by superposition of two waves of same frequency traveling in opposite directions.
- Nodes: Points of zero displacement.
- Antinodes: Points of maximum displacement.
- Resonance occurs when frequency of external force matches natural frequency of system, causing large amplitude oscillations.