The frequency of a wave is inversely related to its wavelength, described by the formula:
\[ f = \frac{c}{\lambda} \]
where:
- \( f \) is the frequency,
- \( c \) is the speed of light (approximately \( 3 \times 10^8 \) meters per second),
- \( \lambda \) is the wavelength.
Given:
- AM waves have a wavelength of approximately 100 m.
- FM waves have a wavelength of approximately 1 m.
Calculation of Frequencies:
-
Frequency of AM Waves: \[ f_{\text{AM}} = \frac{c}{\lambda_{\text{AM}}} = \frac{3 \times 10^8 \text{ m/s}}{100 \text{ m}} = 3 \times 10^6 \text{ Hz} \text{ (or 3 MHz)} \]
-
Frequency of FM Waves: \[ f_{\text{FM}} = \frac{c}{\lambda_{\text{FM}}} = \frac{3 \times 10^8 \text{ m/s}}{1 \text{ m}} = 3 \times 10^8 \text{ Hz} \text{ (or 300 MHz)} \]
Comparison of Frequencies:
- FM waves have a higher frequency (300 MHz) compared to AM waves (3 MHz).
Energy of Waves:
The energy of a photon is given by the formula:
\[ E = h f \]
where:
- \( E \) is the energy,
- \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \) J·s),
- \( f \) is the frequency of the wave.
Since the energy of the wave is directly proportional to its frequency:
- FM waves, having a higher frequency, will also have higher energy compared to AM waves.
Conclusion:
- FM waves have a higher frequency and higher energy than AM waves.
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