# If an FM Radio Station Broadcasts at a Frequency of 101.3 MHz, What is the Wavelength? If an FM Radio Station Broadcasts at a Frequency of 101.3 MHz, What is the Wavelength? The wavelength of an FM radio broadcast at a 101.3 MHz frequency would be 3 meters or 2.96 meters to be precise. And this is how.

FM radio stations broadcast radio waves in the form of electromagnetic waves. Such waves travel at the speed of light and can travel through a vacuum as well. Radio waves’ frequency varies between 30 Hz and 300 GHz. Their high frequency makes radio waves easily transmittable over a long-range. As such, they’re often used in long-range communication.

While arriving at the 2.96 meters wavelength, there are parameters that are already known. For example, the frequency of transmission is 101.3 MHz.

A wave’s wavelength of a particular frequency is expressed as λ=cf where λ represents the radio wave’s wavelength, c the wave’s speed, which is also equal to the speed of light, and f the radio wave’s frequency.

The speed of any electromagnetic wave is equal to that of light, which is:

3 × 108 m / s.

Substituting the values of  c and f in the above equation, we end up with the following:

λ = (3 × 108) / 101.3 MHz

=  (3× 108)/ (101.3×106)

= (3× 108) / (1.013×108)

= 2.962 m

Therefore, the wavelength of a wave of an FM radio broadcasting at a 101.3 MHz frequency is 2.96 meters.

101.3 MHz is, in this case, the frequency at which the radio wave is propagated at a speed of   3 × 108 m / s, or simply 300,000,000 meters per second. And the wavelength would be 2.962 meters as arrived at in the above calculation. However, this wavelength is only applicable in a vacuum setting. If the electromagnetic wave of the radio was traveling in anything else, the wavelength would vary.

When cutting an antenna for a specific frequency, the free space wavelength is first determined before applying a velocity factor correction in order to account for the well-known fact that the wave will travel at different velocities in different materials.

The reality is that any material other than a vacuum slows down the speed of travel. This, in effect, means that even though the frequency varies at 101.3 megacycles every second, its speed through the conductor is much slower and does not travel that long during one cycle. For this reason, the conductor’s length needed to span a wavelength of a given frequency is much less that it would be in free space.

For instance, for a radio signal traveling through an RG-8 coaxial cable, the velocity factor is 86 percent. That means that its wavelength at 101.3 MHz frequency signal would be 0.86 × 2.962 = 2.5473 meters. This, therefore, means that the wavelength through an RG-8 at 101.3 MHz will be 2.5473 meters. Similarly, an RG-213 cable has a velocity factor of 66 percent. For a wavelength of 2.962 meters, this velocity factor would reduce it to 0.66 × 2.962 = 1.9549 meters. Sometimes these differences can be so critical that they have to be considered. One such instance is when constructing a radio antenna.

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