If an FM radio station transmits at 108 MHz, then calculate the wavelength in meters of that radio wave.
The Correct Answer and Explanation is :
To calculate the wavelength of a radio wave, we can use the formula:
[
\lambda = \frac{c}{f}
]
Where:
- (\lambda) is the wavelength in meters (m)
- (c) is the speed of light in a vacuum ((3.0 \times 10^8 \, \text{m/s}))
- (f) is the frequency in hertz (Hz)
Given:
- The frequency of the FM radio station is 108 MHz, which is (108 \times 10^6 \, \text{Hz}).
Now, substituting the values into the formula:
[
\lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{108 \times 10^6 \, \text{Hz}} = 2.78 \, \text{m}
]
So, the wavelength of the FM radio wave is approximately 2.78 meters.
Explanation
The wavelength of a wave is the distance between two consecutive peaks (or troughs) of the wave. It is inversely related to the frequency, meaning that as the frequency increases, the wavelength decreases.
The formula (\lambda = \frac{c}{f}) comes from the fact that waves travel at a constant speed (the speed of light (c)) in a vacuum, and the frequency of the wave tells us how many oscillations occur per second. By dividing the speed of light by the frequency, we obtain the wavelength, which tells us the length of each cycle of the wave.
FM radio waves typically have frequencies ranging from 88 MHz to 108 MHz, and in this case, with a frequency of 108 MHz, the wavelength is relatively short compared to AM radio waves, which operate at lower frequencies (typically 530 to 1700 kHz) and therefore have longer wavelengths.
This shorter wavelength allows FM radio waves to carry more data, providing better sound quality and less susceptibility to interference than AM radio waves. The wavelength of 2.78 meters is typical for FM radio signals, making it suitable for the high-frequency range used by these stations.