Characteristics of Light Waves

Understanding Frequency

• Definition of Frequency: Frequency () is the number of wave cycles that pass a given point per second.
• Wave Cycle: A single complete up-and-down motion of a wave.

Wavelength Relationship

• Definition of Wavelength (): The distance from one wave cycle to the next.
• Comparison of Wavelengths: A longer wavelength means fewer cycles per second, while a shorter wavelength means more cycles.
  • Example: Longer wavelength flashes less frequently; shorter wavelength flashes more frequently.

Measuring Frequency

• Calculation of Frequency:
  • Frequency is calculated by dividing the number of cycles by the time taken (in seconds).
  • Example: If 6 cycles pass in 7 seconds, frequency is
    u = \frac{6 \text{ cycles}}{7 \text{ seconds}} = 0.86 ext{ cycles/second}.
• Units of Frequency:
  • Common units include cycles per second (Hz), which is denoted as s^-1.

Speed of Light

• Speed Definition: The distance light travels in a given time.
• Value of Speed of Light: c = 3 \times 10^8 \text{ m/s} (also referred to as 300 million meters per second).
• Distance Examples:
  • Light from 300 million meters away takes 1 second to reach.
  • Light reflecting from the Moon takes approximately 1.23 seconds to reach Earth.

Relationship between Frequency, Wavelength, and Speed of Light

• Mathematical Relationship: The speed of light is constant, and its relationship to wavelength and frequency is defined as:
  c = \lambda \nu
  where () is wavelength, () is frequency, and c is the speed of light.
• Inverse Relationship:
  • As wavelength decreases, frequency increases, maintaining a constant speed of light.
  • Examples:
  • Wavelength = 1 m; Frequency =
    u = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{1 \text{ m}} = 3 \times 10^8 ext{ cycles/second}
  • Wavelength = 2 m; Frequency =
    u = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{2 \text{ m}} = 1.5 \times 10^8 ext{ cycles/second}
  • Wavelength = 0.5 m; Frequency =
    u = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{0.5 \text{ m}} = 6 \times 10^8 ext{ cycles/second}

Conclusion

• Final Equation Review: The equation \lambda \nu = c (wavelength times frequency equals the speed of light).
• Conceptual Insight: The correlation highlights an exact proportion; decreases in wavelength correspond to proportionate increases in frequency due to the speed of light being a constant.