what is the range of wavelengths for (a) fm radio (88 mhz to 108 mhz) and (b) am radio (535 khz to 1700 khz)?
The Correct Answer and Explanation is :
To calculate the range of wavelengths for FM and AM radio, we use the formula:
[
\lambda = \frac{c}{f}
]
Where:
- (\lambda) = wavelength (in meters)
- (c) = speed of light ((3 \times 10^8) m/s)
- (f) = frequency (in Hz)
(a) FM Radio (88 MHz to 108 MHz)
1 MHz = (1 \times 10^6) Hz, so:
- For 88 MHz ((88 \times 10^6) Hz):
[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{88 \times 10^6 \, \text{Hz}} = 3.41 \, \text{m}
] - For 108 MHz ((108 \times 10^6) Hz):
[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{108 \times 10^6 \, \text{Hz}} = 2.78 \, \text{m}
]
So, the wavelength range for FM radio is approximately 2.78 meters to 3.41 meters.
(b) AM Radio (535 kHz to 1700 kHz)
1 kHz = (1 \times 10^3) Hz, so:
- For 535 kHz ((535 \times 10^3) Hz):
[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{535 \times 10^3 \, \text{Hz}} = 561.68 \, \text{m}
] - For 1700 kHz ((1700 \times 10^3) Hz):
[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{1700 \times 10^3 \, \text{Hz}} = 176.47 \, \text{m}
]
So, the wavelength range for AM radio is approximately 176.47 meters to 561.68 meters.
Explanation
FM (Frequency Modulation) and AM (Amplitude Modulation) radio signals use different frequency bands, and the wavelength of a radio wave is inversely proportional to its frequency. This means that higher frequencies (like those in FM) correspond to shorter wavelengths, and lower frequencies (like those in AM) correspond to longer wavelengths.
FM radio operates in the Very High Frequency (VHF) range, which allows for clearer signals over shorter distances. This is why FM radio typically has better sound quality but requires more infrastructure (like repeaters) to cover large areas.
AM radio, on the other hand, operates in the Medium Frequency (MF) range. Its longer wavelengths allow AM signals to travel further, especially at night when atmospheric conditions change, but it is more prone to static and noise interference due to weather and electrical equipment.
Both AM and FM radios use different parts of the electromagnetic spectrum, and understanding their wavelength ranges helps in the design of antennas and receivers optimized for their respective frequencies.