High School

An FM radio station broadcasts at 98.3 MHz. Calculate the wavelength of the corresponding radio waves.

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.

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-

  1. Frequency of an electromagnetic waves is least for radio waves .
  2. wavelength of an electromagnetic waves is maximum for radio waves.
  3. Penetration power of electromagnetic waves is directly proportional to frequency so radio waves is the weakest one.
  4. Applications of this wave includes satellite communication.
  5. 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

To know more about wavelength of radio waves-

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