Electromagnetic Energy and Waves

Learning Objectives

• Understand the basic behavior of waves.
• Distinguish between traveling waves and standing waves.

Types of Waves

Traveling Waves

• Identification: Follow a point on the wave (like a peak or trough), and observe its motion.
  • The wave moves in a particular direction (e.g., left to right).
• Example: Light as a traveling wave moving through space.

Standing Waves

• Identification: Pick a point on the wave; it doesn't move like in traveling waves.
  • Peaks and troughs invert without net motion.
• Nodes: Points with no net movement, located between peak to trough inversions.

Electromagnetic Nature of Light

• Traveling Wave: Light is a traveling wave in the electromagnetic field.
  • Comprised of perpendicular oscillations in electric and magnetic fields.
• Electromagnetic Radiation: Perpendicular oscillations of electric and magnetic fields.

Fundamental Aspects of Waves

Wavelength (

λ)

• Symbol: Lowercase lambda (λ).
• Definition: Distance between two equivalent points in a wave (e.g., consecutive peaks).

Frequency (

ν)

• Symbol: Greek letter nu (ν).
• Definition: Number of cycles per second; measured in Hertz (Hz).
• Relationship: Inverse relationship with wavelength.

Amplitude

• Definition: Magnitude of the wave's displacement.
  • Measured from the middle imaginary line to the peak or trough.
  • Independence: Amplitude is independent of frequency and wavelength.

Relationship Between Wavelength and Frequency

• Inverse Relationship: When wavelength decreases, frequency increases.
• Speed of Light ( c): Product of wavelength and frequency gives a fixed speed (speed of light, c).
  • Value: 2.998 x 10^8 meters per second.

Practice Problem

• Objective: Determine frequency and wavelength of radiation using given equations.
  • Equation: Wavelength x Frequency = Speed of Light (c).
  • Units and Conversion: Necessary unit conversions (e.g., nanometers to meters).

Quantization

• Definition: Only discrete values from a general set of continuous values are observed.
• Example in Waves:

  • Standing Waves: Fixed points result in discrete frequencies for waveforms.

  • Applications: Important for understanding electronic structure of matter.

These notes cover the essential concepts related to electromagnetic energy and waves, including their behaviors, fundamental aspects, and key differences between types of waves.