Wavelength And Frequency
A radio station broadcasts its signal as electromagnetic waves at a frequency of 100 MHz through the air. What is the approximate wavelength of these broadcast waves?
Select the correct option:
Solution
3 m
All electromagnetic waves in air or vacuum travel at the speed of light, and their wavelength and frequency are tied together by c = f\lambda. Rearranging gives \lambda = c/f. Converting the frequency, 100 MHz equals 1.0 \times 10^{8}\ \text{Hz}, so \lambda = (3.0 \times 10^{8})/(1.0 \times 10^{8}) = 3\ \text{m}. The 30 m option results from forgetting that mega means 10^{6} and treating the frequency as 10^{7}\ \text{Hz}. The 0.3 m value overestimates the frequency by a factor of ten. The 300 m answer would correspond to a frequency of 1 MHz, typical of AM rather than FM broadcasting. Converting between frequency and wavelength using c = f\lambda is a basic requirement of the NCERT Electromagnetic Waves chapter. As a plausibility check, FM radio operates near 100 MHz and indeed has wavelengths of a few metres, so a 3 m result is entirely consistent with everyday broadcasting, confirming both the arithmetic and the unit conversion are correct.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic waves
- Topic
- wavelength and frequency
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
3 m
All electromagnetic waves in air or vacuum travel at the speed of light, and their wavelength and frequency are tied together by c = f\lambda. Rearranging gives \lambda = c/f. Converting the frequency, 100 MHz equals 1.0 \times 10^{8}\ \text{Hz}, so \lambda = (3.0 \times 10^{8})/(1.0 \times 10^{8}) = 3\ \text{m}. The 30 m option results from forgetting that mega means 10^{6} and treating the frequency as 10^{7}\ \text{Hz}. The 0.3 m value overestimates the frequency by a factor of ten. The 300 m answer would correspond to a frequency of 1 MHz, typical of AM rather than FM broadcasting. Converting between frequency and wavelength using c = f\lambda is a basic requirement of the NCERT Electromagnetic Waves chapter. As a plausibility check, FM radio operates near 100 MHz and indeed has wavelengths of a few metres, so a 3 m result is entirely consistent with everyday broadcasting, confirming both the arithmetic and the unit conversion are correct.
This easy difficulty physics question is from the chapter electromagnetic waves, covering the topic of wavelength and frequency. It appeared in the 2025 exam.
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