Problem: An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 108 s−1 (103.1 MHz). What is the wavelength of these radio waves in meters?

FREE Expert Solution
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FREE Expert Solution

We are being asked to calculate the wavelength with a frequency equal to of 1.031 × 108 s−1.

Wavelength, frequency, and the speed of light are connected by the following equation:

$\overline{){\mathbf{c}}{\mathbf{=}}{\mathbf{\lambda \nu }}}$

c = speed of light, m/s
λ = wavelength, in m
ν = frequency, Hz (Hertz)

We can rearrange the equation to isolate the wavelength (λ):

$\frac{\mathbf{c}}{\mathbf{\nu }}\mathbf{=}\frac{\mathbf{\lambda }\overline{)\mathbf{\nu }}}{\overline{)\mathbf{\nu }}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{\lambda }}{\mathbf{=}}\frac{\mathbf{c}}{\mathbf{\nu }}}$

Calculate the wavelength (λ):

Given:

ν = 1.031 × 108 s−1

c = 2.998x108 m/s

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Problem Details

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031 × 108 s−1 (103.1 MHz). What is the wavelength of these radio waves in meters?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Speed of Light concept. You can view video lessons to learn Speed of Light Or if you need more Speed of Light practice, you can also practice Speed of Light practice problems .

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