The formula is wavelength(meters) = 300 / frequency(MHz).
Take 300, divide by frequency, and you will have the wavelength.
The wavelength of the signal broadcast from the FM radio station is [tex]\boxed{2.96\,{\text{m}}}[/tex] or [tex]\boxed{3.0\,{\text{m}}}[/tex] .
Further Explanation:
The radio waves broadcasted by the FM radio station are the electromagnetic waves. The electromagnetic waves are the transverse waves which travel at the speed of light. The electromagnetic waves can also travel through the vacuum.
The frequency range for the radio waves varies from [tex]30\,{\text{Hz}} - 300\,{\text{GHz}}[/tex] . Due to their very high frequency, the radio waves can be easily transmitted over a long range and therefore they are used in the long range communication.
Given:
The frequency of the radio waves emitted by the FM broadcasting station is [tex]101.3\,{\text{MHz}}[/tex] .
Concept:
The wavelength of the wave having a particular frequency is given by the relation:
[tex]\boxed{\lambda=\frac{c}{f}}[/tex]
Here, [tex]\lambda[/tex] is the wavelength of the radio wave, [tex]c[/tex] is the speed of light and [tex]f[/tex] is the frequency of the radio waves.
The speed of the electromagnetic wave is same as that of the speed of light and its value is [tex]3\times{10^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}[/tex] .
Substitute the values of [tex]c[/tex] and [tex]f[/tex] in above expression.
[tex]\begin{aligned}\lambda&=\frac{{3\times{{10}^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}}{{101.3\,{\text{MHz}}\times\left({\frac{{{{10}^6}\,{\text{Hz}}}}{{1\,{\text{MHz}}}}}\right)}}\\&=\frac{{3\times{{10}^8}}}{{1.013\times{{10}^8}}}\,{\text{m}}\\&=2.{\text{96}}\,{\text{m}}\\\end{aligned}[/tex]
Thus, the wavelength of the radio waves emitted by the FM broadcast station is [tex]\boxed{2.96\,{\text{m}}}[/tex] .
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Answer Details:
Grade: College
Subject: Physics
Chapter: Electromagnetic waves
Keywords:
Frequency, broadcast wavelength, radio waves, frequency, 101.3 MHz, electromagnetic waves, 3x10^8 m/s, FM broadcast, speed of light.
