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Answer :
The wavelength of the radio waves from an FM radio station broadcasting at 98.3 MHz is approximately 3.05 meters, using the formula λ = c/f where c is the speed of light and f refers to the frequency of the broadcast.
The question asks for the calculation of the wavelength of the radio waves emitted by an FM radio station broadcasting at a frequency of 98.3 MHz. To find this, we use the formula λ = c/f , where λ is the wavelength, c is the speed of light (approximately 3.0 × [tex]10^8[/tex] m/s), and f denotes the frequency of the broadcast.
Plugging in the numbers, we get: λ = (3.0 × [tex]10^8[/tex] m/s) / (98.3 × [tex]10^6[/tex] s−1) = 3.05 meters.
Therefore, the wavelength of the radio waves from the FM station at 98.3 MHz is approximately 3.05 meters. This is comparable to the size of a car's antenna, and having an antenna size similar to the wavelength ensures better reception of the radio signal.
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The corresponding wavelength of radio waves is 3.03336704 m.
Given - Broadcast Frequency = 98.3MHz
To compute the value of wavelength of the corresponding radio waves following points are considered-
- Frequency of an electromagnetic waves is least for radio waves .
- wavelength of an electromagnetic waves is maximum for radio waves.
- Penetration power of electromagnetic waves is directly proportional to frequency so radio waves is the weakest one.
- Applications of this wave includes satellite communication.
- There is an inverse relation between wavelength and frequency.
Mathematical principle-
[tex]E=hV\\\\E=h\frac{c}{\alpha } \\\\\alpha =wavelength\\c=Light-Speed[/tex]
Calculations-
From this we can derive the formula for frequency -
[tex]V=\frac{c}{\alpha }[/tex]
[tex]\alpha =\frac{c}{V}[/tex]
=3x10⁸ /98.3
=3033367.04/10⁶
=3.03336704 m
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