Lecture Notes: Sinusoidal Waves and Their Importance in Physics

Overview

• Discussion on sinusoidal waves
• Importance in physics
• General equation of periodic waves
• Relation of parameters to physical quantities

Key Topics

• Sinusoidal Waves: Disturbances that carry energy through a medium.
• Wave Equation: Function of space and time, with derivatives concerning time and space.
• Electromagnetic Waves: Involves speed of light (C).

Wave Parameters

• Amplitude: Maximum height of the wave from the mean line.
• Wavelength (λ): Related to wave number (k) by (k = \frac{2\pi}{\lambda}).
• Angular Frequency (ω): Related to linear frequency (ν) by (ω = 2\pi\nu).
• Phase (Φ): Represents the initial angle or offset.

Intensity and Energy

• Intensity: Proportional to the square of the amplitude.
  • Formula: Intensity is energy per unit area per unit time.
  • Relation to power and area.
• Energy Changes: Depends on both amplitude and distance from the source.

Frequency

• Time Frequency vs Spatial Frequency: Time frequency relies on time intervals, while spatial frequency concerns space.

Photoelectric Effect

• Key Concept: Electrons ejected when photon energy exceeds threshold.
• Intensity vs Energy: Increasing intensity doesn't increase energy unless photon energy threshold is met.
• Einstein's Contribution: One photon interacts with one electron.

Practical Examples

• FTIR Spectra: Plotted in wave numbers on the x-axis.
• Phase Shift: Results in different wave properties.

K-Space (Momentum or Reciprocal Space)

• Relevance in Solid-State Physics: Assists in understanding momentum distribution in wave functions.

Simple Harmonic Motion

• Analogies: Circle motion, pendulum, and spring oscillation.
• Equations: Same as those for simple harmonic motion.

Conclusion

• Amplitude affects intensity, but not the inherent energy of individual photons.
• Understanding wave properties is crucial to different fields of physics.