Question

A radio station's channel, such as 100.7 fm or 92.3 fm, is actually its frequency in megahertz (mhz), where 1mhz=106 hz and 1hz=1s−1. calculate the broadcast wavelength of the radio station 88.70 fm.

Answer 1

The broadcast wavelength of radio waves is $\fbox{3.38\,{\text{m}}}$ or $\fbox{338\,{\text{cm}}}$.

Further Explanation:

Radio waves are one of the types of the electromagnetic radiation. It travels with the speed of light in vacuum. The range of frequency of radio waves is very large ranging from $30\,{\text{Hz}}$ - $300\,{\text{GHz}}$.

Radio waves are used to transmitting the signal over a large distance on the Earth. Radio waves can go beyond the line of sight through diffraction and reflection. Radio waves are non ionizing radiation. They have not sufficient energy to separate electrons from atoms or molecules.

Transmitters are used to generating radio waves artificially and antennas are used to receiving the waves.

Given:

The frequency of radio waves is $88.7\,{\text{MHz}}$.  

Concept:

The relationship between frequency and wavelength given by:

$\fbox{\begin\\\lambda=\dfrac{c}{f}\end{minispace}}$

Here, $c$ is the speed of light, $f$ is the frequency of radio waves, and $\lambda$ is the wavelength of radio waves.

Substitute $88.7 \times {10^6}\,{\text{Hz}}$ for $f$ and $3 \times {10^8}\text{ m}/\text{s}$ for $c$ in above equation.

$\begin{aligned}\lambda&=\frac{{3\times{{10}^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}}{{88.7\times{{10}^6}\,{\text{Hz}}}}\\&=3.38\,{\text{m}}\\&= 338}}\,{\text{cm}}\\\end{aligned}$

Thus, the broadcast wavelength of the radio station is $\fbox{3.38\,{\text{m}}}$.

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Answer Details:

Grade: High School

Subject: Physics

Chapter: Electromagnetic waves

Keywords:

Frequency, broadcast wavelength, radio waves, radio station, 88.7fm, speed of light, broadcast, electromagnetic waves, channel. transmitters, 3.38m, 338 cm

Answer 2

The frequency of the radio station is
$f=88.7 fm= 88.7 MHz = 88.7 \cdot 10^6 Hz$

For radio waves (which are electromagnetic waves), the relationship between frequency f and wavelength $\lambda$ is
$\lambda= \frac{c}{f}$
where c is the speed of light. Substituting the frequency of the radio station, we find the wavelength:
$\lambda= \frac{3 \cdot 10^8 m/s}{88.7 \cdot 10^6 Hz}=3.38 m$