Calculating Wavelength from Frequency

Calculating Wavelength from Frequency

Key Concept: Wavelength-Frequency Relationship

• The wavelength of a light wave is inversely proportional to its frequency. This relationship is expressed by the equation: $\lambda = \frac{c}{f}$ where:
  • $\lambda$ = wavelength (in meters)
  • $c$ = speed of light (approximately $3 \times 10^8$ m/s or 300,000 km/s)
  • $f$ = frequency (in Hz)

Example Calculation

• To find the wavelength of a light wave with a frequency of 1 Hz:

  1. Identify the frequency:
  • Given frequency $f = 1$ Hz
  1. Speed of light:
  • $c = 3 \times 10^8$ m/s
  1. Apply the formula:
  • $\lambda = \frac{3 \times 10^8 m/s}{1 Hz}$
  • This results in:
  • $\lambda = 3 \times 10^8 m$

• Therefore, the wavelength of the light wave with a frequency of 1 Hz is 300,000,000 m or 300,000 km.

Answer Options

• 30 km
• 300,000 km
• 30 m
• 300,000 m

Correct Answer

• The correct answer is 300,000 km.

Conclusion

• Understanding the relationship between wavelength and frequency is essential for various applications in physics and engineering, particularly in the areas of optics and telecommunications.