Physics, 04.08.2019 05:30 chickenwing32

An fm radio station broadcasts at a frequency of 101.3 mhz. what is the wavelength?

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Answer from: barnhill4755

The formula is wavelength(meters) = 300 / frequency(MHz).

Take 300, divide by frequency, and you will have the wavelength.

Answer from: PastyMexican24

The wavelength of the signal broadcast from the FM radio station is $\boxed{2.96\,{\text{m}}}$ or $\boxed{3.0\,{\text{m}}}$ .

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 $30\,{\text{Hz}} - 300\,{\text{GHz}}$ . 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 $101.3\,{\text{MHz}}$ .

Concept:

The wavelength of the wave having a particular frequency is given by the relation:

$\boxed{\lambda=\frac{c}{f}}$

Here, $\lambda$ is the wavelength of the radio wave, is the speed of light and 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 $3\times{10^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}$ .

Substitute the values of and in above expression.

$\begin{aligned}\lambda&=\frac{{3\times{{10}^8}\,{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}}}{{101.3\,{\text{MHz}}\times\left({\frac{{{{10}^6}\,{\text{Hz}}}}{{1\,{\text{MHz}}}}}\right)}}\\&=\frac{{3\times{{10}^8}}}{{1.013\times{{10}^8}}}\,{\text{m}}\\&=2.{\text{96}}\,{\text{m}}\\\end{aligned}$

Thus, the wavelength of the radio waves emitted by the FM broadcast station is $\boxed{2.96\,{\text{m}}}$ .

Learn More:

1. A radio station's channel, such as 100.7 fm or 92.3 fm, is actually

2. What is the threshold frequency ν0 of cesium

3. Calculate the wavelength of an electron (m = 9.11 × 10-28 g) moving at 3.66 × 106 m/s

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.

An fm radio station broadcasts at a frequency of 101.3 mhz. what is the wavelength?

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